NISTIR 7856 

Applied and Computational 

Mathematics Division 

Summary of Activities for Fiscal Year 2011 

NISTIR 7856 

Applied and Computational 

Mathematics Division 

Summary of Activities for Fiscal Year 2011 

Ronald F. Boisvert, Editor 

Applied and Computational Mathematics Division 

Information Technology Laboratory 

 http://dx.doi.org/10.6028/NIST.IR.7856 

May 2012 

U.S. Department of Commerce 

John E. Bryson, Secretary 

National Institute of Standards and Technology 

Patrick D. Gallagher, Director 
 
Abstract 

This report summarizes the technical work of the Applied and Computational Sciences Division of 

NIST’s Information Technology Laboratory. Part I (Overview) provides a high-level overview of the 

Division’s activities, including highlights of technical accomplishments during the previous year. Part II 

(Features) provides further details on ten projects of particular note this year. This is followed in Part III 

(Project Summaries) by brief synopses of all technical projects active during the past year. Part IV (Activity Data) provides listings of publications, technical talks, and other professional activities in which 

Division staff members have participated. The reporting period covered by this document is October 2010 

through December 2011. 

For further information, contact Ronald F. Boisvert, Mail Stop 8910, NIST, Gaithersburg, MD 20899-

8910, phone 301-975-3812, email boisvert@nist.gov, or see the Division’s web site at 

http://www.nist.gov/itl/math/index.cfm. 

Cover Visualization: The computational grid for an elliptic boundary value problem whose solution has 

a mild circular wave front. The colors represent the polynomial degree of approximation over each element. The grid comes from a comparative study of automated grid refinement strategies. The strategies 

studied utilize a combination of refinement in space (h) and in polynomial degree (p), termed hprefinement. The study was undertaken by William Mitchell and Marjorie McClain. For details, see page 

27.

Acknowledgement: We are grateful to Robin Bickel for collecting the information and organizing the 

first draft of this report. Thanks also to Timothy Burns and Ashit Talukder for carefully reading through 

the document and providing corrections. 

Disclaimer: Certain commercial entities, equipment, or materials may be identified in this document in 

order to describe an experimental procedure or concept adequately. Such identification is not intended to 

imply recommendation or endorsement by the National Institute of Standards and Technology, nor is it 

intended to imply that the entities, materials, or equipment are necessarily the best available for the purpose. 

Summary of Activities for Fiscal Year 2011 5

Contents 

PART I: OVERVIEW......................................................................................................................... 9

Introduction ............................................................................................................................. 11

Highlights ................................................................................................................................. 13

Technical Accomplishments .................................................................................................. 13

Technology Transfer and Professional Activities ................................................................. 15

Administrative News .............................................................................................................. 16

Recognition ........................................................................................................................... 21

PART II: FEATURES ..................................................................................................................... 25

hp-Adaptive Finite Element Methods ................................................................................... 27

Unsuspected Nonuniqueness in Solving Parabolic Equations Backward in Time ........... 29

Body Area Network Visualization and Analysis .................................................................. 32

Rheology of Dense Suspensions ............................................................................................. 34

Segmentation and Tracking of Breast Cancer Cells ............................................................ 38

Single Photon Up-conversion and Quantum Information Science ..................................... 40

Community and Cluster Detection: Alternative Measures for Network Structure ......... 42

PART III: PROJECT SUMMARIES .................................................................................................. 45

Mathematics of Metrology ..................................................................................................... 47

Unsuspected Nonuniqueness in Solving Parabolic Equations Backward in Time ............... 47

Molecular Movies: Imaging Femtosecond Motion during Electrochemical Transitions ..... 47

Sparse Representations in High Dimensional Geometry ...................................................... 48

Applied Hierarchical Control ............................................................................................... 49

Denoising Helium Ion Microscope Nanoscale Imagery ....................................................... 50

Uncertainty Quantification in Scientific Computing ............................................................. 51

Virtual Measurements in Quantum Chemistry ...................................................................... 52

Bubble Motion and Size Variation during Thermal Migration with Phase Change ............. 53

Shape and Stability of Rotating Toroidal Drops ................................................................... 54

Boundary Slip Effect on the Stability of Spiral Poiseuille Flow ........................................... 55

A Multicomponent and Multiphase Model of Reactive Wetting ............................................ 55

Measurement of the Flow Stress of Carbon Steel for High-Speed Machining Simulations . 56

Modeling the Temperature on the Tool-Chip Interface during High-Speed Machining ...... 57
6 NIST Applied and Computational Mathematics Division 

Simulation of Bioregulatory Networks Involved in Cell Cycle Control ................................ 57

Mathematical Optimization of Procedures for Cryoprotectant Equilibration ...................... 58

A Standard Candle for Extragalactic Metrology ................................................................... 59

Unfolding Optical Spectrum Measurements .......................................................................... 60

Variable Projection for Nonlinear Least Squares Problems ................................................. 61

Shape Analysis ....................................................................................................................... 62

Neural Networks .................................................................................................................... 62

High Performance Computing and Visualization ................................................................ 63

Rheology of Dense Suspensions ............................................................................................. 63

Segmentation and Tracking of Breast Cancer Cells .............................................................. 63

Body Area Network Visualization and Analysis .................................................................... 63

Modeling, Visualization of Cement Paste Hydration and Microstructure Development ...... 63

Measuring Errors in Polygonal Representations of Surfaces ............................................... 65

Processing Large Phantom Image Sets ................................................................................. 66

Visualizing Fire and the Resulting Deformation of Structures ............................................. 67

Nano-structures, Nano-optics, and How to Squeeze the Light out of Quantum Dots ........... 67

3D in Web Pages.................................................................................................................... 68

Information Visualization ...................................................................................................... 69

Scientific Software ................................................................................................................... 70

hp-Adaptive Finite Element Methods .................................................................................... 70

OOF: Finite Element Analysis of Material Microstructures ................................................. 70

Micromagnetic Modeling ....................................................................................................... 71

Parallel Adaptive Refinement and Multigrid Finite Element Methods ................................. 72

Finite Differences Using Voronoi Cells ................................................................................. 73

Digital Library of Mathematical Functions .......................................................................... 74

Digital Library of Mathematical Functions........................................................................... 74

Mathematical Knowledge Management ................................................................................ 75

DLMF Standard Reference Tables on Demand ..................................................................... 76

Visualization of Complex Functions Data ............................................................................. 77

Quantum Information ............................................................................................................. 78

Single Photon Upconversion and Quantum Information Science ......................................... 78

Quantum Computing Benchmarks ......................................................................................... 78

Quantum State Estimation Theory and Applications ............................................................. 79

Quantum State Tomography using Compressed Sensing ...................................................... 80

Quantum Computing Theory ................................................................................................. 80

Quantum Algorithms for Quantum Field Theories ................................................................ 81
Summary of Activities for Fiscal Year 2011 7

Post-Quantum Cryptography ................................................................................................ 82

Foundations of Measurement Science for Information Systems ........................................ 84

Community and Cluster Detection: Alternative Measures for Network Structure ............... 84

Algorithms to Approximate Multivariate Network Reliability .............................................. 84

New Importance Functions and Efficient Algorithms for Network Reliability ..................... 85

Affiliation Networks .............................................................................................................. 85

Degree-Based Modeling ........................................................................................................ 86

Scaling of Congestion in Small World Networks .................................................................. 86

Bootstrap Percolation on Random Geometric Graphs ......................................................... 87

Cross-layer Network Optimization for Diverse QoS Requirements ..................................... 87

Analysis of a Distributed Protocol for an Access Network with Multiple Users .................. 88

Methods that Streamline Search for Failure Scenarios in Large-Scale Systems .................. 89

Advanced Combinatorial Testing for Systems ...................................................................... 90

Security Risk Analysis of Enterprise Networks Using Attack Graphs .................................. 92

Mobile Sensor Networks ....................................................................................................... 92

PART IV: ACTIVITY DATA ....................................................................................................... 95

Publications.............................................................................................................................. 97

Appeared ............................................................................................................................... 97

Refereed Journals ........................................................................................................... 97

Journal of Research of NIST .......................................................................................... 98

Book Chapters ................................................................................................................. 98

Conference Proceedings.................................................................................................. 98

Technical Magazine Articles ........................................................................................ 100

Technical Reports ......................................................................................................... 100

Accepted .............................................................................................................................. 100

In Review ............................................................................................................................ 102

Presentations .......................................................................................................................... 103

Invited Talks ....................................................................................................................... 103

Conference Presentations .................................................................................................. 105

Web Services .......................................................................................................................... 107

Software Released ................................................................................................................. 107

Conferences, Minisymposia, Lecture Series, Shortcourses ............................................... 107

MCSD Seminar Series ....................................................................................................... 107

Hosted Public Events ......................................................................................................... 108

External Events Organization ........................................................................................... 108
8 NIST Applied and Computational Mathematics Division 

Other Professional Activities ................................................................................................ 109

Internal ................................................................................................................................ 109

External ............................................................................................................................... 109

External Contacts .................................................................................................................. 110

PART V: APPENDIX ..................................................................................................................... 113

Staff ......................................................................................................................................... 115

Glossary of Acronyms ........................................................................................................... 118
Summary of Activities for Fiscal Year 2011 9

Part I: Overview

 Part I 

Overview 
10 NIST Applied and Computational Mathematics Division 
Summary of Activities for Fiscal Year 2011 11

Introduction 

Founded in 1901, NIST is a non-regulatory federal agency within the U.S. Department of Commerce. 

NIST's mission is to promote U.S. innovation and industrial competitiveness by advancing measurement 

science, standards, and technology in ways that enhance economic security and improve our quality of 

life. The NIST Laboratory program is broad-ranging, with research efforts in physics, electrical engineering, materials science, chemistry, bioscience, engineering, fire research, and information technology. 

The Information Technology Laboratory (ITL) is one of six major laboratories and user facilities at 

NIST. ITL seeks to (a) accelerate the development and deployment of information and communication 

systems that are reliable, usable, interoperable, and secure; (b) advance measurement science through innovations in mathematics, statistics, and computer science; and (c) conduct research to develop the 

measurements and standards infrastructure for emerging information technologies and applications. 

The Applied and Computational Mathematics Division (ACMD) is one of six technical Divisions in 

ITL. ACMD provides leadership within NIST in the use of applied and computational mathematics to 

solve science and engineering problems arising in measurement science and related applications. In that 

role ACMD staff members 

 perform research and development in applied mathematics and computer science and engineering, 

including analytical methods, numerical and symbolic algorithms, advanced computing and communications architectures and applications, and high performance scientific visualization; 

 engage in peer-to-peer collaborations in the application of mathematical and computational technologies to NIST problems; 

 develop and disseminate mathematical reference data, software, and related tools; and 

 work with internal groups and external organizations to develop standards, test procedures, reference implementations, and other measurement technologies for advanced scientific computation 

on current and future architectures. 

Division staff is organized into four groups: 

Mathematical Analysis and Modeling Group (Timothy Burns, Leader) 

Performs research and maintains expertise in applied mathematics, mathematical modeling, and 

numerical analysis for application to measurement science. 

Mathematical Software Group (Daniel Lozier, Leader) 

Performs research and maintains expertise in the methodology and application of mathematical algorithms and software in support of computational science within NIST as well as in industry and 

academia. 

Computing and Communications Theory Group (Ronald Boisvert, Acting Leader) 

Performs research and maintains expertise in fundamental mathematics, physics, and measurement 

science necessary to enable the development of future computing and communications systems. 

High Performance Computing and Visualization Group (Judith Terrill, Leader) 

Performs research and maintains expertise in the methodologies and tools of high performance scientific computing and visualization for use in measurement science. 

The technical work of the Division is organized into six thematic areas; these are described in the 

sidebar. In addition, ITL has several cross-cutting programs to which the Division contributes: 

 Virtual Measurement Systems. A virtual measurement is a quantitative result and its associated 

uncertainty, obtained by a computer simulation or computer-assisted measurements. This Program introduces metrology constructs, standard references, uncertainty characterization, and 

traceability into scientific computation and computer-assisted measurements to enable predictive 

computing with quantified reliability. 
12 NIST Applied and Computational Mathematics Division 

 Complex Systems. Complex Systems are composed of large interrelated, interacting entities which 

taken together, exhibit a macroscopic behavior which may not be predictable by examining the 

components. This Program seeks to understand the fundamental science of these systems and develop rigorous mathematical and statistical descriptions that enable prediction and control of their 

behavior. 

 Pervasive Information Technology. Pervasive information technology is the trend towards increasingly ubiquitous connected computing sensors, devices, and networks that monitor and 

respond transparently to human needs. This Program creates the mathematical and statistical 

foundations that facilitate the creation of standards for sensor communication, networking interoperability, and sensor information security. 

Division Thematic Areas 

Mathematics of Metrology. Mathematics plays an important role 

in the science of metrology. Mathematical models are needed to 

understand how to design effective measurement systems, and to 

analyze the results they produce. Mathematical techniques are 

used to develop and analyze idealized models of physical phenomena to be measured, and mathematical algorithms are 

necessary to find optimal system parameters. Finally, mathematical and statistical techniques are needed to transform the resulting 

data into useful information. The goal of this work is to develop 

fundamental mathematical methods and analytical tools necessary 

for NIST to continue as a world-class metrology institute, and to 

apply them to critical measurement science applications. 

Scientific Software. Modern science and engineering in general, 

and modern measurement science in particular, requires a wide 

variety of software tools for scientific discovery, exploration, and 

analysis. As scientific inquiry becomes deeper and more specialized, so must the supporting software tools. The goal of this work 

is to develop critical software tools that support measurement 

science at NIST, as well as computational science and engineering at large.

Foundations of Measurement Science for Information Systems. 

Modern information systems are astounding in their complexity. 

Software applications are built from thousands of interacting 

components. Computer networks interconnect millions of independently operating nodes. Large-scale networked applications 

provide the basis for services of national scope, such as financial 

transactions and electrical power distribution. In spite of our 

increasing reliance on such systems, our ability to build far outpaces our ability to secure. Protocols controlling the behavior of 

individual nodes lead to unexpected macroscopic behavior. Local 

power anomalies propagate in unexpected ways leading to largescale outages. Computer system vulnerabilities are exploited in 

viral attacks resulting in widespread loss of data and system 

availability. The long term stability of our critical infrastructure is 

simply unknown. Measurement science has long provided a basis 

for the understanding and control of physical systems. Similar 

types of deep understanding and insight are lacking for complex 

information systems. We seek to develop the mathematical foundations needed for the emergence of a true measurement science 

for complex networked information systems. 

High Performance Computing and Visualization. Computational capability is advancing rapidly. This means that modeling and 

simulation can be done with greatly increased fidelity (e.g., higher 

resolution, more complex physics). However, developing largescale parallel applications remains highly challenging, requiring 

expertise that application scientists rarely have. In addition, the 

hardware landscape is changing rapidly, so new algorithmic techniques must constantly be developed. We are developing and 

applying facilities and expertise of this type for application to 

NIST problems. Large scale computations and laboratory experiments invariably produce large volumes of scientific data, which 

cannot be readily comprehended without some form of visual 

analysis. We are developing the infrastructure necessary for advanced visualization of scientific data, including the use of 3D 

immersive environments and applying this to NIST problems. 

One of our goals is to develop the 3D immersive environment 

into a true interactive measurement laboratory. 

Digital Library of Mathematical Functions. The special functions of applied mathematics are fundamental tools enabling 

modeling and analysis in all areas of science and engineering. To 

make effective use of such functions, practitioners must have 

ready access to a reliable source of information on their properties. The goal of this work is the development and dissemination 

of definitive reference data on the special functions of applied 

mathematics. The centerpiece of this effort is the DLMF, a freely 

available interactive and richly linked online resource.

Quantum Information. An emerging discipline at the intersection 

of physics and computer science, quantum information science 

(QIS) is likely to revolutionize science and technology in the 

same way that lasers, electronics, and computers did in the 20th

century. By encoding information into quantum states of matter, 

one can, in theory, exploit the seemingly strange and counterintuitive behavior of quantum systems to enable phenomenal 

increases in information storage and processing capability, as well 

as communication channels with extremely high levels of security. Although many of the necessary physical manipulations of 

quantum states have been demonstrated experimentally, scaling 

these up to enable fully capable quantum computers remains a 

grand challenge. We are engaged in (a) theoretical studies to 

understand the true power of quantum computing, (b) collaborative efforts with the multi-laboratory experimental quantum 

science program at NIST to characterize and benchmark specific 

physical implementations of quantum information processing, and 

(c) the development and assessment of technologies for quantum 

communication. 
Summary of Activities for Fiscal Year 2011 13

In Part III of this document we provide outlines of most ongoing technical projects of the Division. 

These are organized by thematic area. ITL Programs to which the project contributes are also identified. 

Highlights 

In this section we identify some of the major accomplishments of the Division during the past year. We 

also provide news related to ACMD staff. 

Technical Accomplishments 

ACMD has made significant technical progress on many fronts during the past year. Here we highlight a 

few notable technical accomplishments with significant impact. Further details are provided in Part II 

(Features) and Part III (Project Summaries). 

 Digital Library of Mathematical Functions. The DLMF1

, a major online reference on the special 

functions of applied mathematics, which, along with its print companion, the NIST Handbook of Mathematical Functions, was released in May 2010, continues to garner significant attention. The work has seen 

favorable reviews in SIAM News, SIAM Review, Notices of the American Mathematical Society, Optics 

and Photonics News, and the International Statistical Review. After just 19 months Google Scholar has 

already identified 166 citations to the print edition. In late 2011 the work was recognized with two significant awards: the Department of Commerce Gold Medal and the Government Computer News award for 

IT achievement in government. (See page 74.)

On April 6-8, 2011 ACMD hosted a major conference on this topic. More than 60 researchers in 

the field of special functions from 10 countries and the U.S. participated in the International Conference 

on Special Functions in the 21st Century: Theory and Applications, which was held in Washington, DC. 

The conference provided a forum for the exchange of expertise, experience and insights among world 

leaders on the subject. The conference highlighted the recent release of the DLMF and was dedicated to 

its Mathematics Editor, Frank W. J. Olver. Six plenary and 34 contributed talks were presented. The plenary speakers were Roderick Wong (City University of Hong Kong), Leonard Maximon (George 

Washington University), Nalini Joshi (University of Sydney), Michael Berry (University of Bristol), William Reinhardt (University of Washington), and Richard Askey (University of Wisconsin). The City 

University of Hong Kong, the University of Maryland, and SIAM were co-sponsors. Daniel Lozier of 

ACMD Chaired the Organizing Committee. 

Mathematics of Metrology. ACMD was the host of a second major conference this year, which 

was associated with the ITL Virtual Measurement Systems program. A virtual measurement is a measurement made using a computer simulation model. As in physical measurement, characterizing the 

uncertainty in the measured quantity is of prime concern. This was the main subject of the Working Conference on Uncertainty Quantification in Scientific Computing2

 held in Boulder, CO on August 1-4, 2011, 

where 76 participants representing 10 countries gathered to consider the role of metrology in mathematical modeling and computer simulation. Among the keynote speakers were Pasky Pascual of the US 

Environmental Protection Agency, William Kahan of the University of California at Berkeley, Scott Ferson of Applied Biomathematics, and Maurice Cox of the National Physical Laboratory (UK). 

Applications discussed included cosmology, weather/climate modeling, atmospheric chemistry, hydrology, nuclear energy/safety, fluid dynamics, engineering mechanics, manufacturing processes, medicine, 

toxicology, and computer security. Proceedings will be published by Springer. (See page 51.)

The ITL Virtual Measurement Systems Program also received a boost this year from an interagency initiative in materials science: the Materials Genome Initiative (MGI). The MGI, which was 

announced by the President in June3

, seeks to develop the computational modeling and simulation infra-

 

1 http://dlmf.nist.gov/

2 http://www.nist.gov/itl/math/ifip-woco-10.cfm 3 http://www.whitehouse.gov/blog/2011/06/24/materials-genome-initiative-renaissance-american-manufacturing
14 NIST Applied and Computational Mathematics Division 

structure needed to significantly accelerate the process by which new materials are developed and deployed. One of four participating Federal agencies4

, NIST is expected to play a critical role in several 

areas, including the curation of materials property data, standards for data and software interoperability, 

and the technology and tools for the assessment of quality of computational results. ACMD’s long experience in materials modeling, scientific software development, and its growing competence in uncertainty 

quantification in scientific computing will position it well to make contributions to this effort in the coming years. 

Scientific Software. ACMD, in collaboration with the NIST Materials Measurement Laboratory, 

this year released a new version of its OOF2 software system for modeling materials with complex microstructures. Such materials are composed of many small regions, or grains, with different compositions or 

crystalline orientations. The microscopic shape and arrangement of the grains affects the macro scale 

properties of the material. Users start with a micrograph, which gives the geometry of the grains, and use 

OOF2 to generate a finite element mesh which is then used to calculate various physical properties of the 

material as a whole. The new version, 2.1, can solve for nonlinear and time dependent physical properties, 

including coupled elasticity, thermal conductivity, and dielectricity, on two dimensional material images. 

A three dimensional version is under development. OOF2 was developed by Valerie Coffman, Gunay 

Dogan, and Stephen Langer of ACMD and Andrew Reid of MML. OOF2 can be downloaded5

 at no cost. 

(See page 70.) 

This year ACMD’s software system, PHAML6

, for parallel solution of elliptic partial differential 

equations7

 (PDEs) based on adaptive grid refinement and multigrid methods, was used as a platform for a 

major survey of methods for so-called hp adaptive grid refinement. Adaptive methods are essential for 

successfully attacking the most challenging modeling problems based on PDEs. h-based methods improve 

their solution estimates by refining in space (i.e., reducing size of triangles), while p-based methods refine 

by increasing the polynomial order of approximation on fixed-size grid elements. hp methods combine 

the two. Many heuristics have been proposed for implementing such a refinement strategy. 13 separate 

strategies were evaluated on a battery of 12 test problems. Not only do the results provide useful data on 

the comparative performance of the methods, but they also provide insight on practical tradeoffs between 

efficiency and performance. (See page 72.)

High Performance Computing and Visualization. Our effort to develop a high fidelity modeling 

capability for the simulation of dense suspensions continues. Our model, QDPD, which was developed in 

collaboration with the NIST Engineering Lab, is based on a dissipative particle dynamics approach. This 

is currently being applied to the study of rheometers for measuring flow properties of concrete. A typical 

simulation for this problem may entail keeping track of up to 100,000 solids of varying shape and size. 

The resulting computational complexity requires the use of parallel processing. Our parallel implementation scales well up to 32,000 processors on the Blue Gene/P supercomputer at Argonne National 

Laboratories. Late last year we were awarded an additional 22 million CPU hours for this effort from the 

Department of Energy’s INCITE program8

. (See page 34.)

We continue to refine our growing expertise in image analysis, which is becoming an increasingly important tool in metrology. This year, for example, we worked with colleagues at the National 

Institutes of Health who are studying the migration of cancer cells which can lead to metastasis. Large 

sequences of images are collected to study cell migration, but these are difficult to process manually, and 

existing image segmentation and tracking methods are largely ineffective on cell imagery. We have developed novel image segmentation and cell tracking algorithms for this application. (See page 38.) 

Quantum Information. We continue our efforts to assess both the opportunities and the risks 

posed by quantum engineering. The opportunities include the development of specialized computing de-

 

4 The others are the Department of Energy, the Department of Defense, and the National Science Foundation. 5 http://www.ctcms.nist.gov/oof/oof2 6 http://math.nist.gov/phaml/

7 Ellipic PDEs are ubiquitous in mathematical modeling of numerous processes, including electrostatics, steady-state diffusion, 

pressure fields in fluid flow, and quantum mechanics. 8 http://www.doeleadershipcomputing.org/incite-program/
Summary of Activities for Fiscal Year 2011 15

vices which can solve heretofore intractable problems. A significant risk is that fast quantum algorithms 

for factoring and computing discrete logarithms break the public key infrastructure that is the basis for 

secure online commerce. An important Division effort is the development and application of experimental 

benchmarks for evaluating the practical capability of the many physical systems which have been proposed to effectively quantum compute. One such method for determining an error per unit gate (EPG) for 

one-qubit computations has been implemented on an increasing number of platforms. This year Division 

staff participated in a new implementation of this benchmark in a NIST ion trap where the qubits are manipulated with microwaves instead of laser light. This implementation successfully demonstrated EPGs 

below the critical value of 0.0001, which is believed to be necessary for practical scalable quantum computing. (See page 78.)

Division staff played a critical role in an important demonstration of quantum optical engineering 

critical to future quantum computing applications. In a collaborative effort with NIST’s Center for Nanoscale Science and Technology, Division staff demonstrated for the first time the conversion of nearinfrared 1,300 nm wavelength single photons emitted from a true quantum source, a semiconductor quantum dot, to a near-visible wavelength of 710 nm. Quantum dots have potential both as qubit storage 

devices, as well as reliable photon sources. Converting the color of an emitted photon in this way enables 

highly efficient detection by commercially available detectors. Division staff developed the highly sensitive and efficient upconversion detectors used in this study, which was reported in Nature Photonics. (See 

page 40.)

Our effort to characterize the true power of quantum computers was given a significant boost this 

year with the hiring of two experts in quantum algorithms and complexity theory. One interest will be the 

analysis of computational problems which could serve as a basis for public key cryptosystems which are 

immune to attack by quantum computers. 

Foundations of Measurement Science for Information Systems. We continue to make progress in 

this ACMD initiative which began in FY2007. Our work focuses on characterizing the structure and dynamics of networked information systems. The goal is to understand how these influence network 

performance, e.g., reliability and security. The tools for this work include graph theory, combinatorics, 

discrete dynamics, optimization, and game theory. Examples of our work include the development of 

Monte Carlo approximation methods for combinatorially difficult counting problems, such as computing 

the reliability polynomial of a large graph, the evaluation of methods for community detection in graphs, 

modeling of network routing algorithms, and the optimization of network bandwidth assignments. Finally, we are considering some application areas, such as software testing. (See page 84.)

This year we kicked-off a new collaboration with Bell Laboratories by sponsoring a joint workshop. Some two dozen researchers in a newly emerging subfield of network science gathered together at 

Bell Labs in Murray Hill, NJ on April 26, 2011, at a joint Bell Labs-NIST Workshop on Large-Scale Geometry of Networks. The meeting highlighted current work on fundamental geometric methods in the 

modeling and optimization of complex networks. A particular focus was the hyperbolicity of network 

graphs and its possible impact on network performance, reliability, robustness and security, with the 

eventual goal of creating new metrics for such network characteristics. The workshop featured eight technical presentations from researchers at the University of California at Santa Cruz, the University of 

Southern California, the Cooperative Association for Internet Data Analysis (CAIDA) at UCSD, Rutgers, 

Bell Labs, and NIST. Researchers from AT&T Labs also attended. Eight ACMD staff members participated. The meeting was co-organized by Iraj Saniee of Bell Labs and Vladimir Marbukh of ACMD. 

Technology Transfer and Professional Activities 

The volume of technical output of ACMD remains high. During the last 18 months, Division staff members were (co-)authors of 22 articles appearing in peer-reviewed journals, two book chapters, 33 papers in 

conference proceedings, and nine magazine articles. Thirty-one additional papers have been accepted for 

publication, while 24 others are undergoing review. Division staff members gave 54 invited technical 

talks and presented 40 others in conferences and workshops. 
16 NIST Applied and Computational Mathematics Division 

ACMD continues to maintain an active Web site with a variety of information and services, including the Digital Library of Mathematical Functions, the Guide to Available Mathematical Software, the 

Matrix Market, and the SciMark Java benchmark. During calendar year (CY) 2011, the division web 

server satisfied more than 10.3 million requests for pages from more than 40,000 distinct hosts. In total, 

there have been more than 304 million “hits” on ACMD Web servers since they went online as NIST’s 

first web servers in 1994. The individual software packages that we produce and distribute also continue 

to see very high usage. Table 1 lists download counts for some of our most popular ones. Another indication of the successful transfer of our technology is references to our software in refereed journal articles. 

For example, our OOMMF software for nano-magnetic modeling was cited in 113 such papers which 

were published in CY 2011 alone (more than 1,230 such papers have been identified since 2001). 

Members of the Division are also active in professional circles. Staff members hold a total of 14 editorial positions in peer-reviewed journals. They are also active in conference organization, serving on 10 

organizing/steering/program committees. Staff members organized four minisymposia at technical conferences in 2010. 

Service within professional societies is also prevalent among our staff. For example, Ronald Boisvert serves as Co-Chair of the Publications Board of the Association for Computing Machinery (ACM) 

and is a member of the ACM Council, the association’s board of directors. In addition, staff members 

serve on committees of the IEEE Computer Society, the Mathematical Association of America, the Association for Women in Mathematics, and the Society for Cryobiology. Staff members are also active in a 

variety of working groups. For example, Ronald Boisvert serves as Chair of the International Federation 

for Information Processing (IFIP) Working Group 2.5 on Numerical Software, Donald Porter is a member 

of the Tcl Core Team, Bruce Miller is a member of W3C’s Math Working Group, and Sandy Ressler is a 

member of the Declarative 3D for the Web Architecture Community Group. Judith Terrill represents 

NIST on the High End Computing Interagency Working Group of the Federal Networking and Information Technology Research and Development (NITRD) Program. Robert Bohn is Co-Chair of the 

NITRD Program’s Faster Administration of Science and Technology Education and Research (FASTER) 

Community of Practice. 

For further details, see Section IV, Activity Data. 

Administrative News 

The past year also saw many staffing changes. Among these are the following. 

Arrivals 

Stephen Jordan joined ACMD in April 2011. Jordan comes to ACMD from Caltech, where he was a 

Postdoctoral Fellow in John Preskill’s Quantum Information Group. His thesis, “Quantum Computation 

beyond the Circuit Model,” was done at MIT under the advising of Edward Farhi. At NIST he works on 

quantum computation and post-quantum cryptography. 

Table 1. Downloads of Selected Division Software Packages During CY 2011

Package Description Downloads 

JAMA Linear algebra in Java 33,499 

TNT Linear algebra using C++ templates 8,900 

OOMMF Modeling of nano-magnetic phenomena 5,000 

f90gl Fortran 90 interface to OpenGL graphics 1,945 

spblas Sparse basic linear algebra components 1,388 

OOF Modeling materials with complex microstructure 1,314 

REGEN Modeling of cryocoolers 1,227 

PHAML Parallel adaptive solution of partial differential equations 843 

Ngraph Basic graph algorithms; web crawler 540 
Summary of Activities for Fiscal Year 2011 17

Yi-Kai Liu joined the ACMD staff in May 2011. Liu earned a PhD in Computer Science from the University of California at San Diego where he worked with Russell Impagliazzo and David Meyer on 

quantum complexity theory. Before coming to NIST he held postdoctoral appointments at Caltech and the 

University of California at Berkeley. At NIST Liu will be working on the theory of post-quantum cryptography as well as quantum state tomography. 

Sandy Ressler, Manager of ITL’s Complex Systems Program for the past three years, transferred into 

ACMD’s High Performance Computing and Visualization Group in October 2010. A 25-year NIST veteran, Ressler is an expert in visualization technology. His work has been instrumental in the development 

and standardization of web-based 3D graphics. In ACMD he will develop information visualization techniques, tools, and applications. 

Howard Cohl joined NIST as an NRC Postdoctoral Associate in January 2011. Cohl comes to ACMD 

from the University of Auckland, New Zealand, where he completed a thesis on Fourier and Gegenbauer 

expansions for fundamental solutions of the Laplacian and powers in Rd

 and Hd. Cohl also holds a PhD in 

Physics from Louisiana State. At NIST he is working with Daniel Lozier on rotationally-invariant expansions for solving linear inhomogeneous partial differential equations. 

James Shook joined NIST as an NRC Postdoctoral Associate in July 2011. Shook has a Ph.D. in mathematics from the University of Mississippi where he worked on combinatorics and graph theory. In 

ACMD Shook is working with Brian Cloteaux and Isabel Beichl on the characterization of affiliations in 

networks. 

Asha Nurse joined NIST in January 2011 as a Postdoctoral Fellow supported through the NIST ARRA 

Fellowship Program administered by the University of Maryland. (ARRA is the American Recovery and 

Reinvestment Act.) Nurse comes to NIST from Brown University where she obtained a PhD in solid mechanics. Her thesis dealt with the driving forces for self-assembly of cell clusters and cluster stability. At 

NIST she will be working with Geoffrey McFadden on fluid dynamics applications. 

Assane Gueye, a recent PhD in Computer Science from the University of California at Berkeley, joined 

NIST in the spring of 2011 as a Postdoctoral Fellow supported through the NIST ARRA Fellowship Program. Gueye’s thesis research utilized game-theoretic approaches to study communications security. At 

NIST he will work on game-theoretic models of network dynamics and computer security with Vladimir 

Marbukh. 

Paulina Kuo of the Joint Quantum Institute (a cooperative venture of NIST and the University of Maryland) joined ACMD in October 2011 as a Guest Researcher. Kuo received undergraduate degrees in 

Physics and Materials Science from MIT. In 2008 she received a PhD in Applied Physics from Stanford 

University. She also served as an NRC Postdoctoral Associate in PML. An expert in nonlinear optics, 

Kuo will be contributing to the Division's experimental efforts in quantum communications. 

Ismet Sahin began a term in ACMD as an ARRA Senior Fellow in October 2011. Sahin has a PhD in 

Electrical and Computer Engineering from the University of Pittsburgh (2006). He was most recently a 

Guest Researcher in the NIST National Center for Neutron Research. Sahin will be working with Anthony Kearsley on optimization methods applied to waveform time delay estimation algorithms that are used 

in seismology, radar, sonar, and biomedical science. 

Dennis Backhaus from Fachhochschule Wiesbaden (University of Applied Sciences, Wiesbaden, Germany) began work as a Guest Researcher in the ACMD High Performance Computing and Visualization 

Group. 

Departures 

David Gilsinn has retired from NIST after 40 years of Federal service. After obtaining a PhD in mathematics from Georgetown University in 1969, Gilsinn joined the NBS Technical Analysis Division where 

he worked on railroad crossing risk analysis, flow models for predicting national air cargo and oil pipeline 

flow, models supporting simulation of fires on LP tankers on railcars, and a firehouse location master plan 

for Dade County, Florida. In 1974 he joined the NBS Institute of Computer Science and Technology, 

where he led a team developing conformance tests for commercial BASIC compilers. He also represented 
18 NIST Applied and Computational Mathematics Division 

NIST on the ANSI BASIC subcommittee, leading to the Minimal BASIC Standard in 1978. That year he 

moved to the NBS Precision Engineering Division to work on models of surface roughness, optical scattering from rough surfaces, and image acquisition from scattered laser light. He was also project 

mathematician for the development of the NIST Molecular Measuring Machine. In 1991 he began work 

in the NIST Automated Production Technology Division where, among other things, he worked on mathematical models of machine tools. After 30 years as a mathematician serving in the trenches on foreign 

soil, Gilsinn finally came home to the math division in 2000. In ACMD he worked on computational geometry, L1 spline surface fitting, urban terrain modeling, surface models from LADAR data, and 

construction object recognition. In the last few years he has been working on image processing for medical and biological applications. Gilsinn received the DOC Bronze Medal and the NIST Applied Research 

Award. He produced more than 60 publications, along with the 2009 Springer Book, Delay Differential 

Equations: Recent Advances and New Directions9

 by Balakumar Balachandran, Tamás Kalmár-Nagy, and 

David E. Gilsinn. He also served on the Editorial Board of the ASME Journal of Computational and Nonlinear Dynamics. Gilsinn remains a guest researcher in ACMD. 

Alan Mink, a long time NIST staff member, most recently a member of ACMD’s Computing and Communications Theory Group, retired from NIST in early April 2011. He leaves with an incredible 41 years 

of Federal service. Mink earned a PhD in electronics and communications engineering from the University of Maryland, where he also taught courses in computer architecture. At NIST he worked on a wide 

variety of projects in computer aided design, networking, parallel processing, computer performance 

measurement, cluster computing, digital TV, and quantum communications. Mink is a co-winner of the 

DOC Bronze (2005) and Silver (2008) Medals, the NIST Allen Astin Measurement Science Award 

(1990) as well as the co-recipient of two prestigious R&D 100 Awards (1988 and 2007). He continues to 

contribute to ACMD programs as a guest researcher. 

Valerie Coffman, a former NRC Postdoctoral Associate in ACMD and most recently a term appointee, 

resigned from NIST in July 2011 to devote her energies to her own startup company. In ACMD Coffman 

was a key contributor to the OOF project, which develops software for the modeling of materials with 

complex microstructure. Coffman was leading the development of OOF3D. She has a PhD in Physics 

from Cornell University. 

Peter Ketcham resigned from NIST in October 2011 after service as a mathematician at NIST for 14 

years. During the late 1990s Ketcham worked with David Feder of the NIST Physics Lab and others to 

develop visualizations of models of the newly discovered Bose Einstein condensate. These striking images made their way to the covers of Physics Today, Optics and Photonics News, Parity, and the lead 

illustration in a Scientific American article. In 2000 Ketcham was a joint recipient of the NIST Bronze 

Medal. 

James Benson completed his tenure as a NIST NRC Postdoctoral Associate, accepting a position in the 

Mathematics Department of Northern Illinois University. At NIST Benson worked with Anthony Kearsley on optimal control of heat and mass transfer problems with to application to cryobiology, such as the

improvement of cell cryopreservation protocols. 

Ruediger Kessel completed a three-year term as a Guest Researcher in ACMD, returning to his 

hometown of Braunschweig, Germany, to join the staff of the Physikalisch-Technische Bundesanstalt 

(PTB), NIST’s sister institution in Germany. While at NIST Kessel was active in a wide variety of projects, including calibration of optical sensing devices in satellites, combinatorial testing, definitions of 

metrological consistency, and the development of software for propagating uncertainties using Monte 

Carlo methods. 

Lijun Ma, an ITL guest researcher for seven years, left in October 2011 to take a position as a research 

assistant professor in the Biomedical Engineering Department at Washington University in St. Louis. An 

expert in quantum optics, Ma was a significant contributor to ITL’s experimental efforts in quantum 

communications. An incredibly productive researcher, Ma co-authored 52 papers in journals and confer-

 

9 http://www.amazon.com/Delay-Differential-Equations-Advances-Directions/dp/0387855947
Summary of Activities for Fiscal Year 2011 19

ence proceedings during his six years at NIST. Ma received his PhD in Physics from Tsinghua University 

in China in 2001. He recently became a permanent resident in the US.

Pradeep Reddy Gaddam, guest researcher from Suvojit Chanda, in Navi Mumbai, India, and Clement 

Rey and Guillaume Bousquet, guest researchers from Institut Supérieur d'Informatique, de Modélisation 

et de leurs Applications (ISIMA) in Clermont-Ferrand, France, completed their internships in ACMD. 
20 NIST Applied and Computational Mathematics Division 

During FY 2011 ACMD was able to support the work of 17 student interns, including four in the Student Undergraduate Research Fellowship (SURF) program, three graduate students in Boulder’s 

Professional Research Experience Program (PREP), and two high school volunteers. We also hosted four 

graduate students from French universities, which was facilitated by a Memorandum of Understanding 

signed in late 2009 between ITL and the Institut Supérieur d’Informatique, de Modélisation et de leurs 

Applications (ISIMA) at the University of Clermont-Ferrand. See Table 2 for a complete. 

Table 2. Student Interns in ACMD

Name Institution Level Program Mentor Project Title 

Styvens 

Belloge ISIMA (France) G Guest 

Researcher J. Terrill Visualization and analysis of the National Vulnerability Database 

Guillaume 

Bousquet ISIMA (France) G Guest Researcher F. Hunt Applied mathematics and computational science 

Marlene 

Hildebrand 

Polytech 

(France) G Guest Researcher 

J. Terrill 

A. Peskin Visualization of medical images 

Gregory 

Rami ISIMA (France) G Guest Researcher J. Terrill Impact of fire on building structures 

Jean-Loup 

Traore 

Univ. Blaise 

Pascal (France) G Guest 

Researcher J. Terrill Cement hydration modeling 

Adam 

Meier 

University of 

Colorado G PREP E. Knill Quantum computer simulation 

Michael 

Mullan 

University of 

Colorado G PREP E. Knill Quantum computing theory 

Yanbao 

Zhang 

University of 

Colorado G PREP E. Knill Tests of local realism 

William 

Hess 

Purdue 

University U STEP J. Terrill Lighting in the Immersive Visualization Environment 

Kevin 

Rawlings 

Carnegie 

Mellon Univ. U STEP J. Terrill Visualization and analysis of the National Vulnerability Database 

Anshu 

Rustagi 

University of 

Illinois U STEP W. George Screen Saver Science 

Halley 

Coplin 

Rensselaer 

Poly. Institute U SURF S. Ressler Using the immersive platform to study RF propagation from medical implants 

Gregory 

Herpel 

St. Mary’s 

College U SURF W. George Analysis of a high performance flow of 

suspension code 

Brady 

O’Connell 

University of 

Maryland U SURF R. Bohn Implementation of Use Cases for NIST Cloud Computing Program 

Nadezhda 

Serova UMBC U SURF J. Terrill Dynamics of breaking glass 

Matthew 

Du 

Thomas S. 

Wooton H.S. HS SHIP J. Terrill Spatial distribution of spin in 

nanostructures 

Kevin 

Harrison Poolesville H.S. HS SHIP J. Terrill Impact of fire on building structures 

Legend G: Graduate student 

U: Undergraduate student 

HS: High school student 

SURF: NIST Summer Undergraduate Student Fellowship Program 

 PREP: NIST Professional Research Experience Program
Summary of Activities for Fiscal Year 2011 21

Recognition 

Division staff garnered a number 

of professional recognitions during the past year. These are 

described below. 

The NIST Digital Library of 

Mathematical Functions 

(DLMF) was selected for recognition as an Outstanding 

Information Technology 

Achievement in Government

for 2011 by Government Computer News (GCN). The DLMF 

is the online interactive successor to the classic NBS Handbook 

of Mathematical Functions (M. 

Abramowitz and I. Stegun, eds.) 

published in 1964. The DLMF 

provides reference data on the 

special functions of applied 

mathematics in a concise, usable 

form needed in a wide variety of 

fields, from the physical sciences 

to engineering, biology and finance. The online reference 

features interactive graphics, math-aware search capabilities, and a rich set of internal and external links. 

According to GCN, these awards “have come to symbolize the best and most notable IT accomplishments 

in advancing the work of government agencies.” Ten projects were selected for recognition this year from 

more than 200 nominations. The selection was based on “the degree of innovation in the technology plan 

carried out, the quality of the leadership that carried the project to fruition”, and “the degree to which a 

given IT project improved an agency's ability to operate more efficiently or serve the public more effectively.” Other awardees this year include an app from the City of Boston that enables citizens to request 

city services from their smartphones and the IT infrastructure that supports the TSA’s secure flight program. NIST staff members cited for the DLMF achievement are Daniel Lozier, Frank Olver, Ronald 

Boisvert, Bruce Miller, Bonita Saunders, Marjorie McClain, Abdou Youssef, and Qming Wang of 

ACMD, Brian Antonishek of the ITL Information Access Division, and Charles Clark of the NIST Physical Measurement Laboratory. The project team was formally honored 

at the 24th Annual GCN Awards Gala, October 19, 2011, at the RitzCarlton Tysons Corner in McLean, Va. 

The DLMF team members were also recipients of the Department 

of Commerce Gold Medal for 2011. The Gold Medal is the highest 

honor conferred by DOC. The team was cited for “the development of 

the NIST Digital Library of Mathematical Functions, an unprecedented 

reference on the special functions of applied mathematics.” The award 

was presented by Secretary of Commerce John Bryson on December 

13, 2011. 

Adele Peskin of ACMD was part of a team selected to win the 

Department of Commerce Bronze Medal for 2011. The team was 

cited for “developing innovative techniques that improved the accuracy 

in measurements associated with live cell tracking and image acquisition in cell biology.” The innovations attributed to the team include a 

Figure 1. The Digital Library of Mathematical Functions Team garnered two major recognitions this year. They were cited for producing one of the top 10 IT acheivements in 

government by Government Computer News. They also received the Department of Commerce 

Gold Medal. From left to right: Charles Clark (PML), Brian Antonishek, Marjorie McClain, 

Frank Olver, Qiming Wang, Daniel Lozier, Bonita Saunders, Ronald Boisvert, Bruce Miller, 

Abdou Youssef.

Figure 2. Adele Peskin won a Bronze 

Medal for her work on cell image analysis.
22 NIST Applied and Computational Mathematics Division 

bivariate metric for the evaluation of image segmentation quality, a novel morphological object separation 

technique, a technique for predicting segmentation accuracy for cell images, an accurate overlap-based 

cell tracker, and new techniques for segmenting static and live cell images. 

Ronald Boisvert of ACMD was the recipient of NIST’s Equal Employment Opportunity / 

Diversity Award for 2010. He was cited for “leadership and continuous membership on the ITL 

Diversity Committee and his commitment to fostering diversity. 

Cornelius Lanczos (1893-1974) was selected for recognition by the NIST Alumni Association as part of the NIST 

Portrait Gallery of Distinguished Scientists, Engineers 

and Administrators in October 2010. Frank Olver was 

similarly honored in October 2011. The Gallery honors 

NIST alumni for outstanding career contributions to the 

work of the Institute. Portraits and biographies of those selected are displayed in the corridor of the NIST cafeteria in 

Gaithersburg. Lanczos was a NIST staff member in 1943-

44, participating in the NBS Math Tables Project, and again 

in 1949-52, as a member of the NBS Institute for Numerical 

Analysis. A towering figure in applied mathematics and 

theoretical physics, Lanczos’ best-known contribution to 

science, as measured by citations, was made while at NBS. 

The “Lanczos method” for calculating the eigenvalues of 

large matrices was published in the Journal of Research of 

NBS in 1950. 

Olver was recruited by Milton Abramowitz in 1961 to 

be the author of the chapter “Bessel Functions of Integer 

Order” in the NBS Handbook of Mathematical Functions

(M. Abramowitz and I. Stegun, eds., 1964), a publication 

which went on to become the most widely distributed and 

most highly cited publication in NIST’s history. Olver left 

NIST for the University of Maryland in 1986, though he 

returned to NIST in 1986 as a guest researcher. He is currently a faculty appointee in ACMD. Olver is particularly 

known for his extensive work in the study of the asymptotic 

solution of differential equations. He is author of six books 

(three as editor), two book chapters, 72 journal articles, 27 

papers in proceedings, and nine book reviews. His wellknown and well-regarded book, Asymptotics and Special 

Functions, originally published by Academic Press in 1974 

and translated into Russian in 1978, was reprinted in the 

AKP Classics Series by AK Peters in 1997. In 2000, a 

1,074-page commemorative volume Selected Papers of 

F.W.J. Olver, Parts 1 and II was published by World Scientific Publishing Co. More than half of the 56 reprinted 

papers, originally published from 1949 through 1999, cite 

an NBS affiliation. More recently he served as the Editorin-Chief and Mathematics Editor of the online NIST Digital 

Library of Mathematical Functions and its 966-page print 

companion, the NIST Handbook of Mathematical Functions (Cambridge University Press, 2010). 

Three ACMD staff members were honored in ITL’s annual awards ceremony in 2011: 

 Alfred S. Carasso received the ITL Best Journal Paper Award based on the single authored manuscript, “Bochner Subordination, Logarithmic Diffusion Equations, and Blind Deconvolution of 

Figure 3. Cornelius Lanczos (top) and Frank Olver 

(bottom) were inducted into the Portrait Gallery of 

Distinguished NIST Alumni. 
Summary of Activities for Fiscal Year 2011 23

Hubble Space Telescope Imagery and Other Scientific Data,” which appeared in the refereed journal SIAM Journal of Imaging Sciences, Volume 3, Number 4, 2010, pp. 954-980.

 The inter-Divisional team of Dr. Daniel Genin (ITL/ANTD), Dr. Vladimir Marbukh (ACMD), and 

Dr. Anastase Nakassis (ITL/ANTD) received the ITL Best Conference Paper Award based on the 

manuscript, “Vulnerability of Selfish Routing to Attacks: Game-theoretic Models and Initial Results,” which was presented at the 2010 International Conference of Information Security and 

Internet Engineering held in London on June 30 – July 2, 2010.

 Oliver Slattery of ACMD received the Outstanding Contribution to ITL Award for his outstanding efforts in safety, both as a member of the NIST laser safety committee as well as for his 

leadership in laboratory safety within ITL.

Dianne O’Leary, Professor of Computer Science at the University 

of Maryland and a faculty appointee in ACMD, was selected as the 

Norbert Wieier Lecturer by Tufts University for 2011. The Norbert 

Wiener Lectures were instituted to celebrate one of Tuft’s most wellknown alumni. A world renowned mathematician, Norbert Wiener may 

be most well-known for founding the science of cybernetics. The term 

he coined is the root of now common neologisms such as cyberspace 

and cybersecurity. As the Wiener Lecturer, O’Leary presented three 

lectures on consecutive days, beginning on March 29. The lectures were 

entitled “Mathematics in Words and Images: The role mathematics 

plays in searching the web and in restoring blurred images,” “Uncertainty Quantification for Ill-posed Problems,” and an undergraduate 

seminar “Where Am I? Position from incomplete distance information, 

from Gauss's geodesy problems to protein structures.” Previous Wiener 

Lecturers have included Persi Diaconis (Stanford), Nick Trefethen (Oxford), Jim Yorke (University of Maryland), and Margaret Wright 

(NYU). 

Florian Potra, Professor of Mathematics at the University of Maryland Baltimore County and a faculty appointee in ACMD, was 

recognized in a special commemorative session at the 2011 Spring 

Southeastern Section Meeting of the American Mathematical Society 

held at Georgia Southern University on March 12-13, 2011. The session, which was entitled, “Advances in Optimization,” was organized 

in honor of Potra’s 60th birthday. The session spanned two days of the 

conference. Potra presented the first one-hour lecture, which was entitled “Interior point methods in wide neighborhoods of the central 

path;” this was followed by 14 30-minute presentations on current research in optimization theory and applications. 

The paper: J. Bullard, E. Enjolras, W. George, S. Satterfield and J. 

Terrill, “A Parallel Reaction-Transport Model Applied to Cement Hydration and Microstructure Development,” Modelling and Simulation 

in Materials Science and Engineering, volume 18 (2010), article 

025007 (16pp), was selected as one of the 10 highlights of the journal

for 2010 and collected together on a highlights page10. According to 

IOP Publishing, the paper was one of the most frequently downloaded 

of the year, and “exemplifies the high standard of research that 

MSMSE attracts.” George, Satterfield, and Terrill are ACMD staff members. Enjolras was an ACMD 

guest researcher. 

 

10 http://iopscience.iop.org/0965-0393/page/Highlights%20of%202010

Figure 4. ACMD Faculty Appointee 

Dianne O’Leary was named Norbert 

Weiner Lecturer by Tufts University. 

Figure 5. ACMD Faculty Appointee 

Florian Potra’s 60th birthday was commemorated by a special session of the 

AMS’ Southeast Section meeting. 
24 NIST Applied and Computational Mathematics Division 

A biography of and an extensive interview with ACMD mathematician Fern Hunt have appeared as a chapter in the new book, 

Fascinating Mathematical People: Interviews and Memoirs, edited 

by Donald Albers and Gerald Alexanderson, and published this year 

by Princeton University Press11. Hunt is one of 16 mathematicians 

profiled in the volume. In her interview she describes what it was like 

to be among the first black women to earn a PhD in mathematics. 

Others profiled include Tom Apostol (Caltech), Jean Taylor (Rutgers), and Don Saari (University of California at Irvine). Apostol is 

the author of a chapter in the NIST Digital Library of Mathematical 

Functions, while Taylor and Saari are former frequent visitors to 

NIST. 

 

11 http://press.princeton.edu/titles/9527.html

Figure 6. Fern Hunt’s biography is featured in a new book. 
Summary of Activities for Fiscal Year 2011 25

Part II: Features 

 

 Part II 

 Features 
26 NIST Applied and Computational Mathematics Division 
Summary of Activities for Fiscal Year 2011 27

hp-Adaptive Finite Element Methods 

The numerical solution of partial differential equations 

is the most compute-intensive part of a wide range of 

scientific and engineering applications. So the development and application of faster and more accurate 

methods for solving partial differential equations is a 

very important field that has received much attention in 

the past fifty years. Many of the applications at the 

cutting edge of research are extraordinarily challenging. These problems necessitate the use of the most 

advanced numerical techniques including adaptive grid 

refinement and high order finite elements. Recent research on adaptive grid refinement has resulted in 

several approaches to the so-called hp version of the 

finite element method. We have studied these methods 

and performed an extensive numerical experiment to 

compare their convergence rates and determine which 

methods are most effective in different situations. 

William F. Mitchell 

To solve partial differential equations (PDEs) numerically one divides the domain of the problem into small 

subregions called elements and approximates the solution over each element with a polynomial. To resolve 

difficult features in the solution such as steep fronts, 

highly oscillatory regions, or singularities, the elements 

must be small and/or the polynomial degree must be 

large, but if one does this uniformly over the whole 

domain the number of algebraic equations (degrees of 

freedom) explodes and the problem becomes intractable. It is necessary, then, to use high degree and/or 

small elements only where required. Unfortunately, to 

optimize the element size and degree one must know 

the solution to the PDE. An alternative is adaptive grid 

refinement: start with a coarse, low degree grid, compute a solution, estimate the error in each element, subsubdivide elements with unacceptably large error, and 

repeat. This process, known as h-adaptive refinement 

because h represents the size of the elements, has been 

studied for many years and is widely used in practice 

today. Recent research has improved this algorithm by 

allowing the option of increasing the polynomial degree, denoted p, in an element instead of subdividing it. 

This is known as hp-adaptive refinement. The attraction of hp adaptivity is that, with a suitably chosen hp

grid, the error can converge exponentially in the number of degrees of freedom, N, i.e., 

1/ 3

1

C2N

hp e C e 

for some C1 and C2>0 independent of N, as opposed to 

a polynomial rate for h-adaptive refinement with fixed 

p, i.e., 

/ 2

2

p N

h e C e 

 . 

This implies that one can use a much smaller value of 

N for a given error tolerance, and hence solve the problem much more quickly. 

The difficulty is in determining how to suitably 

choose the hp grid. The local error estimate can be 

used to determine which elements should be refined, 

the same as in h-adaptive refinement, but it cannot 

simultaneously determine how to refine the element, 

i.e. whether it should be subdivided (h-refined) or have 

the polynomial degree increased (p-refined). Methods 

for making that determination are called hp-adaptive 

strategies, and have been the subject of considerable 

research. We identified 13 hp-adaptive strategies in the 

literature. 

Figure 7. Example hp-adaptive grids for two strategies for a solution with a mild circular wave front. The colors represent the 

polynomial degree over each element. Notice that one strategy was 

heavily biased toward p-refinement while the other was biased 

toward h-refinement.
28 NIST Applied and Computational Mathematics Division 

Many of the strategies are based on the premise 

that one should use h-refinement near singularities and 

other strong features, and p-refinement where the solution is smooth. If one has a priori knowledge of these 

features in the solution, it is easy to guide the refinement in this way, but this is rarely the case. Several 

strategies attempt to approximate the smoothness of the 

solution. This is done by examining error estimates for 

approximations with different polynomial degree, and 

using them in a mathematical expression based on the 

theoretical convergence rates. 

Other strategies use a number of different ideas on 

how to estimate which type of refinement will be most 

effective. One of them attempts to formulate the decision globally as an optimization problem: minimize the 

error subject to several constraints, such as placing an 

upper bound on the number of degrees of freedom, and 

requiring that the polynomial degree be positive. Unfortunately the optimization problem is NP hard and 

contains unknown quantities (e.g. the error), so many 

approximations must be made to formulate a tractable 

problem. Another strategy separates the h and p refinement by performing just h-refinement until the 

estimated error has been reduced by a given amount, 

and then just p-refinement until the final tolerance is 

reached. Another strategy uses error estimators to estimate whether h-refinement or p-refinement of an 

element will reduce the error the most. Two strategies 

compute a reference solution by performing uniform hand p-refinement of the entire grid, and project that 

solution onto several candidate refinements to estimate 

which candidate is most effective in an error reduction 

vs. increased cost measure. These strategies are different than the others in that they allow for decreasing the 

polynomial degree in elements that are h-refined. 

The PDE solver PHAML developed by William 

Mitchell of ACMD is based on adaptive refinement 

and contains an implementation of all these hpadaptive strategies. We used this code to perform a 

numerical experiment to compare the effectiveness of 

the strategies in terms of accuracy vs. degrees of freedom. For this experiment we gathered a collection of 

12 test problems [1], most of which came from the 

numerical results section of papers on hp-adaptive refinement. These contain a variety of difficulties 

including singularities, sharp peaks, wave fronts, oscillations and boundary layers. Most of them are 

parameterized to adjust the problems in the experiment. 

Figure 7 illustrates two examples of hp grids 

adapted to a solution that contains a mild circular wave 

front. The black lines show the elements of the grid and 

the colors indicate the degree of the polynomial in each 

element. These grids were generated by different strategies for the same problem, and demonstrate how very 

different the resulting grids can be. 

In anticipation that different strategies would work 

best in different situations, the results of the experiment 

are grouped into six categories: problems with a mild 

difficulty, a strong difficulty, singularities, each at a 

low accuracy requirement (10-2 relative error) and high 

accuracy requirement (10-6 relative error). Summary 

results will be published in [2], with the full results 

available in [3]. The experiment showed that which 

strategies are most effective is dependent on the characteristics of the problem and accuracy requirement. 

An example is shown in Figure 8. For this problem we 

see that the REFSOLN_EDGE strategy is clearly superior. But also notice how T3S is the worst strategy at 

low accuracy, but one of the best at high accuracy. 

One interesting result is that the reference solution 

strategies performed exceptionally well in all categories. However, they are much more computationally 

expensive than the other strategies, which offsets the 

reduction in number of degrees of freedom. This suggests that future research on the development of a more 

effective hp-adaptive strategy should be directed towards using some aspects of these methods to obtain 

their convergence rates without having to compute the 

expensive reference solution. 

References 

[1] W.F. Mitchell, A Collection of 2D Elliptic Problems for 

Testing Adaptive Algorithms, NISTIR 7668, 2010. 

[2] W.F. Mitchell and M.A. McClain, A Comparison of hpAdaptive Strategies for Elliptic Partial Differential 

Equations, submitted.

[3] W.F. Mitchell and M.A. McClain, A Comparison of hpAdaptive Strategies for Elliptic Partial Differential 

Equations (long version), NISTIR 7824, 2011. 

Participants 

William Mitchell, Marjorie McClain (ACMD). 

http://math.nist.gov/phaml/

Figure 8. The convergence plots for all strategies for the problem 

with a very steep wave front. 
Summary of Activities for Fiscal Year 2011 29

Unsuspected Nonuniqueness in Solving Parabolic Equations 

Backward in Time

An iterative procedure originating in the field of spectroscopy has been successfully applied to solve 

nonlinear parabolic equations backward in time. This 

has led to the discovery of previously unsuspected one 

dimensional examples of well-behaved, physically 

plausible, but completely false reconstructions of the 

initial data at time t=0, given approximate values for 

the solution at time t=1. Even more striking examples 

of false reconstructions are likely in multidimensional 

problems. Such examples are of considerable significance in hydrologic inversion and image deblurring, 

two important areas of application of backward parabolic equations. These examples indicate that highly 

detailed prior information about the correct solution is 

likely to be a necessary ingredient in many backward 

reconstruction problems. Such detailed prior 

knowledge may not always be available. 

Alfred Carasso 

There has been growing interest in recent years in the 

development of numerical methods for solving parabolic equations backward in time. Currently, the two 

most significant areas of application of backward parabolic equations are hydrologic inversion and image 

deblurring. In hydrologic inversion, the aim is to identify sources of groundwater pollution by reconstructing 

the contaminant plume history. This involves solving 

the advection dispersion equation (ADE) backward to 

time t=0, given the contaminant spatial distribution 

g(x,y) at the current time t = 1. In scientific and medical 

applications, images blurred by Gaussian point spread 

functions are a common occurrence. Deblurring Gaussian blur is mathematically equivalent to solving the 

heat conduction equation backward in time, with the 

noisy blurred image g(x,y) as data at time t = 1, and 

with conduction coefficient  > 0 proportional to the 

point spread variance. Of continuing interest at NIST 

and other U.S. Government research facilities, is the 

successful application of time-reversed fractional and 

logarithmic diffusion equations in blind deconvolution 

of nanoscale scanning electron microscope imagery, as 

well as cosmological scale Hubble Space Telescope 

imagery. 

While several useful backward parabolic numerical methods exist, no method can avoid the inherent 

practical difficulty that only approximate values can 

generally be known for the solution at the current time 

t=1. Thus, one must reconstruct the past from imprecise knowledge of the present. How such imprecision 

may affect the reconstruction is seldom considered in 

practice. 

Given a well-posed linear or nonlinear parabolic 

equation wt = Lw, t>0 and approximate data f(x) at time 

t = 1such that in the L2 norm, 

w(.,1)  f  

where 

0    w(.,0)  M , 

what can be said about the expected accuracy in backward reconstruction from the given data f ? The 

following fundamental uncertainty inequality for the 

difference of any two possible reconstructions w1

(x,t) 

and w2(x,t), from the given approximate data f, is 

known: 

(., ) (., ) 2 , 0 1 ( ) 1 2 1 ( )      w t w t M t t t   

Here the dependence of the Hölder exponent μ(t) on t, 

shown in Figure 9A, plays a crucial role. In the best 

possible case, that of a linear self adjoint elliptic operator L with time-independent coefficients (blue line), we 

have μ(t) = t, so that μ(t) decays linearly to zero as $t↓

0. This implies a progressive loss of accuracy as reconstruction proceeds from t=1 to t=0. Much more severe 

loss of accuracy may occur in non self adjoint or nonlinear problems (red curve), where the decay in μ(t) is 

sublinear. Moreover, no matter how small δ is, no accuracy can be guaranteed at t=0 since μ(0) = 0. 

The above inequality necessarily contemplates 

worst case scenarios that may be too pessimistic in 

some applications. Indeed, highly useful enhancements 

of nanoscale electron micrographs and Hubble galaxy 

images have been documented. Nevertheless, the behavior of μ(t) in Figure 9A reflects a basic underlying 

truth about parabolic problems. An iterative procedure 

has been developed that can illuminate the deeper 

meaning of the above uncertainty inequality. That iteration can be used to uncover previously unsuspected 

examples of specific one dimensional parabolic equations with distinct solutions wred(x,t) and wgreen(x,t), 

having the property that their traces wred(x,1), 

wgreen(x,1) at t=1 are visually indistinguishable, while 

their corresponding initial values wred(x,0), wgreen(x,0) 

are vastly different. Such an example is shown in Figure 9B, and discussed further below. 

Van Cittert iteration. Given the linear or nonlinear parabolic equation wt = Lw, t > 0, let S be the 

associated solution operator at time t = 1. Thus, given 

initial values h(x) at t = 0, S[h] = wh(x,1), the corresponding solution of the parabolic equation at t = 1. 
30 NIST Applied and Computational Mathematics Division 

Using efficient numerical parabolic solvers, the operation S[h] can be accurately calculated at mesh-points, 

given any h(x). With approximate data f(x) at t = 1 such 

that 

w(.,1)  f    w(.,0)  M , 

we may try to reconstruct the initial value h(x) = w(x,0) 

through the following iteration: 

( ) ( )  ( )  ( ), 1 1      h x h x f x S h x n n n n 

where γ > 0 is a fixed relaxation parameter, and h1

(x) = 

γ f(x). The above Van Cittert iterative procedure is often used in spectroscopy, where S is an explicitly 

known linear convolution operator. The successful 

application of that procedure in nonlinear parabolic 

equations, where S is not known explicitly, was unanticipated. In fact, the Van Cittert iteration seldom 

converges. However, in many cases, the procedure 

generates a sequence of iterates hn

(x) such that the L∞

norm of the residual, || f – S[hn

] ||∞ decays quasi monotonically to a small value after finitely many iterations. 

Figure 9. (A) Linear and sublinear behavior in Hölder exponent. (B) Vastly different red and green initial values at t=0, produce approximately 

the same result at t=1. 

Figure 10. Distinctly different evolutions of red and green initial values at t = 0 into almost identical blue curve at t = 1.
Summary of Activities for Fiscal Year 2011 31 

This is often sufficient for our purpose. If for some 

positive integer N we find 

f S[h ] , with h M , N N    

then hN

(x) is a valid candidate reconstruction of w(x,0), 

given the approximation f(x) to w(x,1). 

Highly Plausible, Yet False Reconstructions. The 

following numerical experiment is one of dozens of 

similar experiments that were performed on one dimensional linear and nonlinear parabolic partial 

differential equations. Here, a strongly nonlinear equation with the initial data wred(x,0) shown in Figure 9B, 

was accurately solved numerically up to time t = 1 to 

produce wred(x,1), shown as the black curve f(x) in Figure 9B. Using f(x) as given approximate data at t = 1, 

the Van Cittert iteration was pursued for 50 iterations 

resulting in an L∞ residual of 4.4 ×10-2. The last iterate 

h50(x) = w0

green(x) is the green trace in Figure 9B. We 

stress that w0

green(x) is a valid reconstruction of the 

unknown initial data, given the approximation f(x) at t

= 1. Indeed, using w0

green(x) as initial data in our parabolic solver reproduces the black curve at t = 1 in 

Figure 9B to within 4.4 ×10-2 pointwise, and L2 relative 

error 2.75 ×10-2. Given the data error levels δ likely to 

be found in typical engineering applications, such an L2 

relative error for the reconstruction seems quite reasonable. Moreover, both red and green curves in Figure 9B 

have an L∞ norm of about 13. 

In Figure 2A, the evolution of w0

green(x) into the 

blue curve at t = 1, is distinctly different from the evolution of w0

red(x) into the almost identical blue curve in 

Figure 2B. Indeed, given the blue curve at t = 1, the 

green evolution seems highly plausible, while the red 

evolution seems improbable. We note that smoothness 

and/or positivity constraints are often applied to regularize backward reconstructions. Here, the 

reconstructed false green evolution is both smooth and 

positive at all times. 

References 

[1] A.S. Carasso, Reconstructing the Past from Imprecise 

Knowledge of the Present: Some examples of Non 

Uniqueness in Solving Parabolic Equations Backward in 

Time, Journal of Research of the NIST, to appear. 
32 NIST Applied and Computational Mathematics Division 

Body Area Network Visualization and Analysis 

Body Area Networks (BANs) consist of RF-enabled 

wearable and implantable sensory nodes for short 

range reliable communication in or around the human 

body. This technology is poised to be a promising interdisciplinary technology with novel uses in pervasive 

health information technology. This project provides 

tools for modeling and visualizing the propagation of 

the signals on which the networks’ wireless communications depend. Our recent work on BAN visualization 

and analysis is shedding light on: the effect of other 

types of medical implants on BAN signal propagation; 

path loss in BAN communications channels; and the 

creeping wave phenomenon as it affects body surface 

signal propagation. This work is assisting IEEE standards committees and will help RF engineers to design 

more effective network devices. 

John Hagedorn 

Body Area Networks (BANs), which are networks operating near or within the human body, are an emerging 

technology that has potential in a variety of application 

areas. Perhaps the most important use for BANs is in 

pervasive heath IT where they will enable continuous 

remote monitoring of a person's health status (such as 

heart rate, blood pressure, etc.) as well as active therapeutic devices such as precision drug delivery. 

Furthermore, BAN is an important technology for the 

implementation of electronic health records; data from 

medical BANs can be sent directly into electric records 

without the need for human data entry. So, BAN technology is poised to become a significant piece of the 

health IT puzzle. 

We seek to advance the state of BAN technology 

by providing tools for understanding RF propagation 

through and near the human body. This understanding 

is essential in developing the devices and protocols that 

will be used in BANs. Our work is supporting the IEEE 

committees that are developing the communications 

standards for BANs as well as the RF engineers who 

are designing the network communications devices. 

There are two intertwined parts of this work on 

BAN technology. The first part is the simulation of RF 

propagation through the human body; the second part 

is the visualization and analysis of the data produced 

by these simulations. The work within ACMD is mostly focused on the visualization and analysis. 

We perform simulations of RF propagation because experiments involving implanting devices in 

human subjects are not feasible. The modeling is 

achieved using a commercially available 3D full-wave 

electromagnetic field simulator. A detailed 3D human 

body model is used which includes frequencydependent dielectric properties of over 300 parts in a 

male body. 

We have developed a three dimensional immersive 

visualization system to support the investigation of 

these RF propagation results. This system creates a 3D 

virtual environment that enables the user to interact 

directly with the body model and the RF data. We have 

developed interactive tools for quantitatively probing 

these data. This immersive virtual environment and our 

interactive tools are described elsewhere [1, 2]. 

We recently simulated the effect of an artificial 

aortic heart valve implant on communications among 

BAN devices on the surface of the body. In Figure 11 

we show a visualization of a ring that approximates the 

metallic portion of an artificial aortic valve. 

We performed simulations of ultra-wide band 

(UWB) signal propagation based on this valve placement and the placement of a BAN transmitter and 

several receivers on the upper body [3]. The simulations correspond to experiments conducted by our 

collaborators at the University of Oulu, Finland. Simulations and experiments were run both with and 

without the aortic implant. 

The effect of the aortic implant is clear in both the 

simulation and experimental data. (See Figure 12 for a 

Figure 11. A metal ring placed in the body model to simulate the 

presence of an aortic valve replacement.
Summary of Activities for Fiscal Year 2011 33 

visual comparison of the simulations.) However experimental and simulation data do not exactly match; see 

our paper [3] for more detailed results. We will continue to investigate the effect of other medical implants 

on BAN signal propagation. 

Another part of this effort has involved the creation of statistical path loss models for BAN 

communication channels [4]. These models are based 

on simulations of four near surface and two deep tissue 

implant applications using our 3D model of the human 

body. The path loss models obtained in this study have 

been adopted by the IEEE 802.15 task group TG6. The 

accuracy and applicability of such models will require 

further validation and investigation. 

Much of our current work centers on applications 

in which BAN devices are attached or worn on the surface of the body. In this situation, the creeping wave 

phenomenon comes into play which affects how signals propagate along surfaces. We are investigating 

how the creeping wave effect may be exploited for onbody BAN devices. This may effect antenna design and 

device placement decisions. 

Our visualizations and analyses of the simulations 

showed a pronounced creeping wave effect. We then 

performed simulations using a transmitting antenna 

design optimized to exploit the creeping wave. The use 

of these results to compare antenna designs proved 

problematic. We are currently studying how to resolve 

these problems. 

In addition to the continuing effort on the issues 

described above, we are pursuing several lines of investigation. We are collaborating with researchers who 

are doing related experimental work that will help us to 

validate our simulations. We are also developing methods for placing our 3D body model into various poses 

so that we can study the effect that positions and body 

motions have on signal propagation. While this work is 

in an early stage, these simulations will help researchers and engineers understand the issues that affect 

BAN communication. 

References 

[1] Mathematical and Computational Sciences Division, 

Summary of Activities for Fiscal Year 2009, R. Boisvert, Ed., NISTIR 7671, February 2010. 

[2] W.-B. Yang, K. Sayrafian-Pour, J. Hagedorn, J. Terrill, 

and K. Y. Yazdandoost, Simulation Study of Body Surface RF Propagation for UWB Wearable Medical 

Sensors, in Proceedings of the 2nd International Symposium on Applied Sciences in Biomedical and 

Communication Technologies, November 24-27, 2009, 

pp. 1-6. 

[3] W. Yang, K. Sayrafian-Pour, J. Hagedorn, J. Terrill, K. 

Yazdandoost, A. Taparugssanagorn, M. Hämäläinen, 

and J. Iinatti, Impact of an Aortic Valve Implant on 

Body Surface UWB Propagation: A Preliminary Study, 

in Proceedings of the 5th International Symposium on 

Medical Information and Communication Technology, 

March 27-31, 2011, pp. 84-88. 

[4] K. Sayrafian-Pour, W. Yang, J. Hagedorn, J. Terrill, 

K.Y. Yazdandoost, and K. Hamaguchi, Channel Models 

for Medical Implant Communications, International 

Journal of Wireless Information Networks 17 (2010), 

pp. 105-112. 

Participants 

John Hagedorn, Judith Terrill (ACMD); Kamran Sayrafian-Pour, Wen-Bin Yang (ITL); Kamya Yekeh 

Yazdandoost, Attaphongse Taparugssanagorn, Matti 

Hämäläinen, Jari Iinatti (University of Oulu, Finland) 

http://www.nist.gov/itl/math/hpcvg/ban.cfm

Figure 12. The image on the left shows simulated path loss 

without the aortic valve implant. On the right is the same simulation with the valve implant. The rectangle in the middle of the 

chest is the position of the transmitter and the spheres show the 

positions of the receivers in the experiments.
34 NIST Applied and Computational Mathematics Division 

Rheology of Dense Suspensions 

Understanding the mechanisms of dispersion or agglomeration of particulate matter in complex fluids, 

such as suspensions, is of technological importance in 

many industries such as pharmaceuticals, coatings, 

and concrete. These fluids are disordered systems consisting of a variety of components with disparate 

properties that can interact in many different ways. 

Predicting the flow of such systems via mathematical 

models represents a great scientific and computational 

challenge, requiring large scale simulations at a fundamental level. In collaboration with scientists in 

NIST's Engineering Laboratory (EL), we are developing an application, called QDPD (Quaternion based 

Dissipative Particle Dynamics), which is capable of 

performing large scale simulations of dense suspensions. QDPD is highly parallel and has been shown to 

efficiently scale up to at least 32 thousand processors 

when running on the DOE supercomputer Intrepid at 

Argonne National Laboratory. Our goal in this project 

is to advance our understanding of the flow properties 

of a specific system, fresh concrete, a dense suspension 

composed of cement, water, sand, and rocks. 

William L. George 

Nicos Martys 

Concrete is the most widely used building material in 

the world, representing a 100 billion dollar industry in 

the US that is crucial for our nation’s physical infrastructure. There is now a strong interest in making 

concrete a more sustainable material by finding new 

ways to recycle it, and by changing its ingredients in 

order to reduce the amount of greenhouse gas from its 

production. (The manufacture of concrete’s key ingredient, cement, is responsible for about 8% to 10% of 

global CO2 production.) As new mixture designs of 

concrete are developed to meet these needs, it is important to measure and control rheological properties, 

i.e. flow properties, to satisfy performance specifications. Failure to control the flow of concrete on a job 

site can lead to significant cost overruns and months of 

delay by having to correct previous errors. 

Often fluids are characterized by the properties 

yield stress and viscosity, which are a function of shear 

rate. In particular: yield stress is the force applied per 

unit area to initiate the flow, and viscosity is the applied force per unit area needed to maintain a shear 

rate. Shear rate is the velocity gradient perpendicular to 

the flow direction. An image showing the local stress 

in a vane rheometer is shown in Figure 13. 

Many factors control viscosity and yield stress. 

For example, in building materials like concrete, viscosity and yield stress depend on the ratio of water to 

cement, the volume of sand or rocks used, as well as 

their shape and size distribution. There can be great 

variation in each material depending on their history 

and where they were obtained. For example, rocks 

from quarries are usually angular because they are 

crushed when processed, whereas rocks obtained from 

river beds are typically rounded due to erosion. Additionally, the more similar the size of the rocks in a 

concrete suspension, the harder it is to get the concrete 

to flow. In this case, the concrete may actually jam 

when poured through a narrow opening, thus causing 

delays in construction. Clearly, to optimize the flow 

properties of concrete and other suspensions, one needs 

Figure 13. Snapshot of a simulation of a 4-blade vane rheometer 

with a suspension of hard spheres. The hard spheres are colored 

by the octant in which it is initially located within the rheometer. 

Spheres from two of these octants have been omitted to show the 

blades of the rheometer. This is the original configuration of a 

simulation of a mortar. 
Summary of Activities for Fiscal Year 2011 35 

to understand the relationship between flow and properties of the fluid's constituents. 

Our current focus is on enabling the use of vane 

rheometers for measuring the rheological properties of 

fresh concrete, something that is not currently possible. 

While different “concrete rheometer” measurements 

can be found to correlate, they usually do not agree 

well in actual measurements in fundamental units. A 

vane geometry combined with a strongly random suspension will result in complex local stress and 

strain/strain rate fields. Simulations will enable us to 

map out these fields in 3D, and bring insight into the 

vane design process. There is no expectation that current vanes are optimized for precise measurement (or 

mixers for best mixing practice), and the results from 

simulations can be used to optimize vane design. We 

are also using simulations in the design process for new 

standard reference materials (SRMs) which will be 

used for calibrating rheometers. This year we completed NIST SRM 2492 – Cement Paste. 

QDPD. Modeling and predicting the flow of suspensions such as concrete represents a great scientific 

challenge since these are complex disordered systems 

with a variety of components that can interact in many 

different ways. Indeed, accounting for the size and 

Figure 14. A snapshot of a vane rheometer simulation displayed with a volume visualization of the magnitude of the local stress within the

system. As in Figure 13, the suspended spheres are color coded by the octant they started in. Only 4 of the 8 octants are shown here in order to 

see details around the vanes. For the added volume visualization, stress is color coded from yellow (low stress), to green (high stress), with 

stresses below a set threshold not shown. The blades of the rheometer are rotating clockwise. 
36 NIST Applied and Computational Mathematics Division 

shape variation of the solid components of the suspension (cement particles, sand, or rocks) poses many 

computational challenges. A representative system may 

entail keeping track of up to 100,000 solids of varying 

shape and size. Further, many of the forces between 

particles depend on the local surface curvature of the 

aggregate at points close to neighboring aggregates, 

which requires keeping track of the location, orientation and shortest distance between neighboring solids. 

Clearly, modeling such systems necessitates large scale 

simulations at a fundamental level to accurately predict 

its properties. We have adopted and developed some 

novel approaches, originally based on cellular automata 

methods, which can successfully take into account 

many of the features of a suspension. Our original 

code, QDPD, has been validated by both theory and 

experiments on idealized systems, and has been extended to account for random shaped objects with 

different inter-particle interactions. 

QDPD [1], which stands for Quaternian-based 

Dissipative Particle Dynamics (DPD), uses modified 

versions of the recently developed DPD technique [2], 

for the simulation of Newtonian fluids, and the 

Smoothed Particle Hydrodynamics technique (SPH) 

[3], for the simulation of non-Newtonian fluids, to 

simulate dense suspensions such as cement paste, mortar, and concrete. In addition to the forces computed 

using the DPD and SPH techniques, other forces are 

computed in these systems to better account for the 

interaction between the inclusions (the large particles) 

in the suspensions. These additional forces include 

lubrication forces that help keep the inclusions separated, and van der Waals forces that introduce an 

attractive interparticle force. Brownian forces are also 

present in QDPD to maintain system temperature. 

From the original serial version of this simulator 

we have enhanced QDPD to utilize the power of large 

parallel machines, regularly using 500+ processors, 

and, for large production runs, using 32 thousand processors. QDPD remains under constant development to 

improve its capabilities as well as to improve its parallel performance. 

Argonne National Laboratory's DOE Leadership 

Computing Facility. During the 2011 calendar year 

we have had access to the 164,000 processor IBM Blue 

Gene/P supercomputer Intrepid, having been awarded 

25 million CPU-hours of compute time on this machine 

from the DOE Innovative and Novel Computational 

Impact on Theory and Experiment (INCITE). This access has enabled us to perform several very large 

simulations of a four-blade vane rheometer. We have 

been awarded a second year of compute time, for 2012, 

on Intrepid through our peer-reviewed INCITE proposal. 

Results. Through numerical modeling and visualization, this research has provided insights into the 

physical mechanisms associated with the onset of flow. 

Aspects of yield stress and viscosity can be linked to 

spatio-geometric properties of suspensions including 

the number of neighboring rocks and their relative orientation. Further, by examining the very long time 

scale behavior of the rocks, we can link their motion to 

visco-elastic properties of the suspension. 

Over the last few years our simulations have provided fundamental insights into mechanisms that 

control the onset of flow in suspensions that can be 

linked to macroscopic properties such as yield stress 

and viscosity. We have developed a novel way of describing the interparticle stress fields and their spatial 

correlations. Though this, it was discovered that under 

shearing, although the suspended particles remain in a 

liquid order, the interparticle stress is strongly anisotropic [4]. In addition, a transition under flow was 

observed: during a transient regime at low deformation, 

the stress propagates along the compression direction 

of the shear, whereas at larger deformations the stress 

is organized into layers parallel to the flow direction. 

Further we have found that yield stress is shear rate 

dependent [5]. The higher the shear rate the greater the 

yield stress. However, in the limit of zero shear rate, 

yield was found to go to zero as a consequence of temperature effects. 

We have recently modeled cementitious materials 

composed of cement and fly ash [6]. Here we studied 

the effect on flow properties of substituting 10% of 

cement with fly ash. To do this we modeled a system 

of angular shaped particles (cement) combined with 

smaller spheres (representing ultra fine fly ash) and 

found that there is a decrease in yield stress and viscosity of the suspension in comparison the same system 

without fly ash. 

Figure 15. The visosity of a suspension, comprised of a proposed 

standard reference material (SRM 2492) + 1 mm diameter glass 

beads, is shown for various volume fractions from 0.00 % (i.e., pure 

fluid matrix) to 49%.
Summary of Activities for Fiscal Year 2011 37 

Our studies have enabled us to discover that, given 

the properties of the matrix non-Newtonian fluid in a 

dense suspension, such as a mortar or concrete, we can 

predict the rheological properties of those dense suspensions. In Figure 15 the visosity of a suspension, 

comprised of a proposed standard reference material 

(SRM 2492) of + 1 mm diameter glass beads, is shown 

for various volume fractions from 0.00 % (i.e., pure 

fluid matrix) to 49 %. Figure 16 shows these plots 

collapse onto the 0 % volume fraction curve using the 

same function to collapse each curve to the “universal 

curve” for this matrix fluid. 

Finally, while the main thrust of our research focuses on predicting the rheological (flow) properties of 

cement based materials such as concrete, an improved 

general understanding of rheological properties derived 

from this research should have a broad impact. Suspensions are utilized in wide variety of technological 

processes and, as our study is largely parametric in 

nature, results will be transferable to other suspensions 

of interest such as nanoparticle systems. Understanding 

mechanisms for the dispersion or agglomeration of 

such systems remains a challenge in many industries 

ranging from pharmaceuticals to coatings. 

References

[1] N. Martys, Study of a Dissipative Particle Dynamics 

Based Approach for Modeling Suspensions, Journal of 

Rheology 49:2 (2005), pp. 401-424. 

[2] P.J. Hoogerbrugge and J.M.V.A. Koelman, Simulating 

Microscopic Hydrodynamic Phenomena with Dissipative Particle Dynamics, Europhysics Letters 19 (1992), 

pp. 155-160. 

[3] J.J. Monaghan, Smoothed Particle Hydrodynamics. 

Reports on Progress in Physics 68 (2005), pp. 1703–

1759. 

[4] N.S. Martys, D. Lootens, W. George and P. Hebraud, 

Contact and Stress Anisotrophies in Start-Up Flow of 

Colloidal Suspensions, Physical Review E 80 (2009), article 031401. 

[5] N.S. Martys, M. Khalil, W. George, D. Lootens, and P. 

Hebraud, Stress Propagation in a Concentrated Colloidal 

Suspension under Shear, EuroPhysics Letters, submitted. 

[6] N.S. Martys, Multiscale Modeling of the Flow of Cement Based Materials, in State-of-the-Art Report on 

Numerical Simulations of Fresh Concrete Flow, 

RILEM, August 2010. 

[7] N.S. Martys, W. George, B. Chun, and D. Lootens, A 

Smoothed Particle Hydrodynamics-Based Fluid Model 

with a Spatially Dependent Viscosity: Application to 

Flow of a Suspension with a Non-Newtonian Fluid Matrix, Rheologica Acta 49:10 (2010), pp. 1059–1069. 

[8] J.W. Bullard, E.J. Garboczi, W. L. George, N. S. Martys, 

S. G. Satterfield, and J. E. Terrill, Advancing the 

Materials Science of Concrete with Supercomputers, 

Concrete International 33:1 (2011). 

Participants

William George, Steven Satterfield, Marc Olano, Judith Terrill (ACMD); Nicos Martys, Edward Garboczi 

(EL); Pascal Hebraud (CNRS/ESPCI, France). 

http://www.nist.gov/itl/math/hpcvg/rheology.cfm

http://www.nist.gov/itl/math/hpcvg/concretevis.cfm

Figure 16. The curves in Figure 15 collapse onto the 0% volume 

fraction curve using the same function to collapse each curve to the 

'universal curve' for this matrix fluid. 
 38 NIST Applied and Computational Mathematics Division 

Segmentation and Tracking of Breast Cancer Cells

The ability of cells to migrate varies widely during the 

development and life of multicellular organisms. Celland organ-specific regulation of the migratory behavior of cells is critical. In normal epithelia, such as 

breast epithelium, cell migration is restricted, but epithelial cells that are transformed into tumor cells 

acquire mutations that allow them to migrate into the 

surrounding connective tissue (invasive tumor) and 

then to distant sites to establish metastatic disease [1]. 

Investigating the migratory behavior of epithelial and 

tumor cells may enable biologists to find ways to control migration of tumor cells and reduce metastasis. 

We have developed new techniques to automatically identify and track individual cells within images of a 

breast cancer cell line in order to study cell migration 

and metastasis. Within each image observable cell 

characteristics vary widely, ranging from very bright 

completely bounded cells to barely visible cells with 

few to no apparent boundaries. A set of different segmentation algorithms are used in series to identify each 

cell type. Normally cell segmentation and tracking are 

performed as two separate steps. However, in this work 

they are done simultaneously so that predictions can be 

made about where cell boundaries lie on an image at 

each time step. A new method for background subtraction is described and a new method of selective dilation 

is used to segment the barely visible cells. Initial results are encouraging. 

Adele Peskin 

Cell migration can be studied by visualizing cell responses through the capture of time-lapse images for 

long periods of time. Quantitative analysis of these 

images is performed by tracking the position of individual cells, a labor-intensive process which can only 

be done manually for a few selected cells. Images from 

the cell line in this study, MCF10CA1a [2], do not lend 

themselves to well known automated segmentation and 

tracking methods. The goal of this work is to automate 

these processes in order to better understand the cell 

migration in this cell line. 

The difficulties in processing these images are 

several-fold. The individual cells move at varying 

speeds, sometimes quite rapidly, making them hard to 

track from image to image over time. The morphologies of the cells themselves vary greatly over a single 

image. As shown in Figure 17, a typical image of these 

cells contains cells that are bright with dark edges that 

are straightforward to segment, along with cells that are 

barely visible at times, so that their apparent shape 

changes over the course of a few minutes. 

We have developed segmentation techniques to 

identify individual cells and track them from image to 

image at early growth times. The steps involve background removal, predicting cell size and location based 

on the previous image in time, and then defining the 

new location and shape. Background removal in a 

timed series is often accomplished by examining the 

whole series to find examples of each part of the background when it is free of cells [3]. However, to process 

in real time it is important to be able to remove background noise for each individual image. For each 

image, a mean value is found for the image as a whole, 

and all pixels with intensity higher than three standard 

deviations above the mean (where cells are located) are 

temporarily replaced by the mean value to smooth out 

the image. Then the background value for each individual pixel is determined by the average value in a 

small neighborhood of that pixel. Figure 18 shows an 

image at the start of growth, color-coded by pixel intensity, before and after background removal. 

Figure 19 shows sections of an image containing a 

variety of cell morphologies. The dark cell boundaries 

and brighter cell areas are easily captured by looking 

for clusters of pixel intensities significantly above and 

below the mean value of the image. The larger pixel 

clusters that represent cell boundaries and cell bodies 

are distinguished from much smaller background clusters by a new method of selective dilation that diffuses 

only the larger clusters to slightly larger shapes to sepaFigure 17. An early image in a time series and a later image.

Figure 18. Sample image color-coded before and after background removal. The color table at the right shows pixel intensities 

before background removal. 
Summary of Activities for Fiscal Year 2011 39 

rate them. To segment the barely visible regions, clusters of pixels are defined whose intensities in very 

localized regions have higher than average standard 

deviations. These clusters are matched with the predicted locations of cells from past time steps. The 

software keeps track of cells that are actively moving 

and their current velocities in past time steps, as well as 

the size and shapes of each cell. Cell velocities are used 

to predict cell locations at the next step. To enhance the 

high standard deviation clusters, the new technique of 

selective dilation is also applied. The total number of 

cells in an image can only vary from time step to time 

step if cells move into or out of the field of view at the 

images boundaries, or if cells divide. It is also important to keep track of cells that die, but remain in the 

field of view. Dead cells have characteristic morphologies and in general no longer move or change shape. 

Recognition of dead cells is important because there is 

no need to track their shape changes and behaviors. 

The details of the segmentation and cell tracking, 

which are performed simultaneously, are given in [4]. 

For short periods of time, we are able to track every 

cell in our test set of images. Cell divisions are identified during the cell tracking, which is an important 

feature. Figure 20 shows some example images and 

their corresponding segmentation/tracking. 

Future work will include larger scale tests and 

comparisons with manually collected data. We are developing a more general model so that we can segment 

and track cell lines with large masses of cells with individual cells whose boundaries go into and out of the 

field of vision of the microscope over time. 

References

[1] C.L. Chaffer and R.A. Weinberg, A Perspective on Cancer Cell Metastasis, Science 331 (2011), pp. 1559–64. 

[2] F.R. Miller, S.J. Santner, L. Tait, and P.J. Dawson, 

MCF10DCIS.com Xenograft Model of Human Comedo 

Ductal Carcinoma in situ. Journal of the National Cancer Institute 92 (2000), pp. 1185–6. 

[3] I. Simon, C.R. Pound, A.W. Parin, J.Q. Clemnes, and 

W.A. Christens-Barry, Automated Image Analysis System for Detecting Boundaries of Live Prostate Cancer 

Cells, Cytometry 31 (1998), pp. 287–294. 

[4] A.P. Peskin, D.J. Hoeppner, and C.H. Stuelten, Segmentation and Cell Tracking of Breast Cancer Cells, In: 

Proceedings of the 7th International Symposium on Visual Computing 2011. (G. Bebis et al. (Eds.): ISVC 2011, 

Part I, Lecture Notes in Computer Science 6938, pp. 

381-391. Springer, Heidelberg (2011). 

Participants

Adele P. Peskin (ACMD); D. J. Hoeppner, C. H. 

Stuelten (National Institutes of Health) 

http://www.nist.gov/itl/math/hpcvg/cellimgvis.cfm

Figure 19. Sub-sections of the image in Figure 2, showing different 

cell morphologies. 

Figure 20. Images and resulting masks at 0, 10, 20, and 30 minutes. 
 40 NIST Applied and Computational Mathematics Division 

Single Photon Up-conversion and Quantum Information Science

Photons play an important role in quantum information 

science. Information can be stored in their quantum 

states (e.g., polarization), and their mobility enables 

these states to be transported over long distances. As a 

result, reliable generation and detection of single photons are important enablers of quantum information 

science and engineering. Photons with wavelengths in 

the near infrared (NIR) are ideal for long-distance 

communication since they suffer the least loss in optical fiber. Unfortunately, commercially available 

detectors are very unreliable at these wavelengths. 

To address this problem, the ITL quantum communication research team has developed novel single 

photon detectors in the NIR range and significantly 

improved their performance in recent years. These 

detectors are based on so-called up-conversion technology, in which the photon’s wavelength is converted 

to one where detectors are efficient, without changing 

essential properties, such as the quantum state in 

which information is encoded. 

Such detectors have wide application in both 

quantum information and in metrology. Using the upconversion detectors the team has performed several 

otherwise difficult or impossible quantum optical 

measurements. The team is working with US industry 

to commercialize the technology via the NIST Small 

Business Innovative Research (SBIR) program. 

Xiao Tang 

Upconversion12 is a process by which two optical fields 

combine in a nonlinear medium to generate a third field 

at a frequency equal to the sum of the two inputs. As 

well as energy conservation, this process requires momentum conservation, placing a condition on the phase 

velocities of the three beams. Recently, it has been 

shown that quasi-phase-matching, a process in which a 

grating in the nonlinear medium is used to compensate 

for wave vector mismatch between the sum frequency 

beam and the two input beams, can enable highly efficient upconversion, with near unity conversion 

efficiencies achieved in periodically poled LiNbO3

(PPLN) waveguides. Because upconversion can, in 

principle, be used to transduce one photon at a given 

wavelength to a photon at another wavelength, one 

could imagine using it to couple different quantum 

systems at different energies. This kind of hybrid quantum-information scheme enables the use of photons for 

efficient transmission of quantum information over 

large distances, and robust, stationary quantum systems 

 

12 Part of this introduction is taken from [3]. 

such as trapped atoms or ions, atomic ensembles, or 

spins in quantum dots for manipulation and storage. 

Another important application of quantum transduction 

is the frequency upconversion of telecommunicationsband photons (e.g., a wavelength of 1310 nm) to the 

visible part of the spectrum (e.g., 850 nm) for detection 

with commercially available low-noise silicon avalanche photo diode (Si-APD) detectors, for example, as 

part of a quantum information protocol. While photons 

at 1310 nm are ideal for long-distance transmission 

over optical fibers, photon detectors are extremely inefficient at that wavelength.

A few years ago, the ITL quantum communication 

research team adapted this technology to develop upconversion detectors at NIST. In 2007, the research 

team successfully demonstrated their use in a fiberbased high speed quantum cryptographic key distribution (QKD) system. Since then, the devices have been 

significantly improved. For example, during the past 

year, the detection noise level, or so called dark count 

rate (the detector records events even if there is no signal input), has been significantly reduced by an order 

of magnitude [1]. As another example, the team developed a multi-wavelength pumping scheme that 

increases the system data rate beyond the barrier set by 

the performance limitations of the Si-APD detectors 

[2]. In addition, using our up-conversion detectors, the 

team performed several otherwise difficult or impossible quantum optical measurements. These include: the 

characterization of semiconductor quantum dots; the 

measurement of higher (second-, third- and fourth) 

orders of photon temporal correlation; and optical sampling at the single photon level using a pulsed upconversion technique. These results demonstrate that 

our up-conversion technique enables advanced quantum optics research with applications in future quantum 

computing and quantum communications systems. 

In quantum information science, individual photons can be used as information carriers. Therefore, the 

study and development of single photon sources has 

become a key research area and opportunity. Semiconductor quantum dots can emit photons one at a time 

and have high potential as practical single photon 

sources. In 2010, the team conducted a joint experiment in collaboration with NIST colleagues in the 

Center for Nanoscale Science and Technology (CNST). 

The up-conversion detectors were used to detect single 

photons at 1310 nm from a semiconductor quantum 

dot. Because of the high sensitivity and low dark count 

rate, our up-conversion detector is able to measure the 

quantum dot exciton lifetime with a much higher accuracy than by using commercial indium gallium arsenide 

(InGaAs)-based detectors typically used at such frequencies. A photon correlation measurement is a good 
Summary of Activities for Fiscal Year 2011 41 

way to characterize a source and to determine whether 

or not it is emitting single photons. By using the upconversion detectors, the team performed a second 

order intensity correlation measurement for the photons 

emitted from the quantum dot and demonstrated for the 

first time that the converted photons preserve their 

quantum characteristics during frequency conversion. 

In FY2011, this important conclusion was reported in 

Nature Photonics [3]. 

To further prove this result, the ITL team, in collaboration with researchers in CNST and the NIST 

Physical Measurement Laboratory (PML), conducted 

higher (2nd, 3rd and 4th) order correlation measurements 

for photons from an attenuated pseudo thermal source 

(similar to a lamp) and a coherent source (attenuated 

laser) in the NIR region. Use of ITL’s detectors proved 

critical, since otherwise it would be very difficult or 

nearly impossible to measure such higher-order correlations due to the lack of suitable commercial detectors 

for photons in the NIR region. Our results, published in 

Optics Express [4], nicely match with theoretical predictions. Figure 21 shows the fourth order correlation 

of photons from the pseudo thermal source. 

The integration of two disparate quantum systems 

requires that the photons from the two systems must 

have same wavelength and same spectral linewidth (so 

called indistinguishable). As described above, upconversion provides the capability to convert or adjust 

the photon’s wavelength. The question then arises, “is 

it possible to adjust the linewidth?” To answer this 

question, the ITL team has collaborated with CNST 

and demonstrated an optical sampling process at the 

single photon power level to accomplish this [5]. Frequency up-conversion devices can be operated with a 

pulsed pump. When a pump pulse width is narrower 

than the signal pulse, in general, it can be viewed as a 

gate for optical sampling. In this process, the photon 

wavelength is transduced and the amplitude profile of 

the photon wave packet is simultaneously modulated 

by the pump pulse shape. The amplitude modulation 

can be used to select the coherent part of the single 

photon wave packet (or change of the linewidth) which 

enables us to make two independent photons perfectly 

indistinguishable. This allows a better integration of 

two disparate quantum systems, which is essential for 

future quantum networks and long distance quantum 

communications. 

Currently, the ITL quantum communication research team is exploring new areas of quantum 

research by using their up-conversion technique, as 

well as working with US industries for its commercialization through the NIST SBIR program. 

References

[1] Xiao Tang, Lijun Ma and Oliver Slattery, Ultra Low 

Dark-Count-Rate Up-Conversion Single Photon Detector, in Proceedings of the IEEE Photonics Society 23rd

Annual Meeting, Denver CO, November 2010. 

[2] Lijun Ma, Joshua C. Bienfang, Oliver Slattery and Xiao 

Tang, Up-Conversion Single-Photon Detector using 

Multi-wavelength Sampling Techniques, Optics Express 

19(6) (2011), p. 5470. 

[3] Matthew T. Rakher, Lijun Ma, Oliver Slattery, Xiao 

Tang and Kartik Srinivasan, Quantum Transduction of 

Telecommunications-Band Single Photons from a Quantum Dot by Frequency Upconversion, Nature Photonics

4 (2010), pp. 786-791. 

[4] Lijun Ma, Matthew T. Raker, Martin J. Stevens, Oliver 

Slattery, Kartik Srinivasan, and Xiao Tang, Temporal 

Correlation of Photons Following Frequency Upconversion, Optics Express 19 (11) (2011), article 

10501. 

[5] Matthew T. Rakher, Lijun Ma, Marcelo Davanço, Oliver 

Slattery, Xiao Tang, and Kartik Srinivasan, Simultaneous Wave-Length Translation and Amplitude 

Modulation of Single Photons from a Quantum Dot, 

Physical Review Letters 107 (2011), article 083602. 

Participants

Lijun Ma, Oliver Slattery, Barry Hershman, Alan 

Mink, Xiao Tang (ACMD); Martin J. Stevens, Joshua 

C. Bienfang (PML); Matthew T. Rakher, Marcelo Davanço, and Kartik Srinivasan (CNST). 

Figure 21. Frame from a movie showing the measured fourth-order 

photon correlation function for a pseudo-thermal source. The function 

has four-dimensions. In addition to the x and y dimensions we use color 

as the third dimension, and present it in a movie showing time as the 

fourth dimension. To view the movie, go to 

http://www.nist.gov/itl/quantum/quantum.cfm
 42 NIST Applied and Computational Mathematics Division 

Community and Cluster Detection: Alternative Measures for 

Network Structure 

Detecting community structure in large graphs is one 

of the fundamental challenges in network science. A 

“community” is loosely defined as a subset of nodes 

which are highly connected to each other, but less connected to other nodes in the graph. Identifying such 

groups can be useful in understanding graph structure, 

as well as its dynamic characteristics, such as evolution and synchronization. In various application 

contexts, community detection can classify persons or 

objects with unifying characteristics. Some examples 

include identifying groups in social networks, determining graph layouts for visualization, and modeling 

the spreading of infectious diseases. In this project we 

are assessing the performance of the many community 

detection algorithms that have been proposed. In the 

course of this work we have uncovered a novel framework for describing the fundamental structure of such 

networks. 

Roldan Pozo 

Extracting community structure reliably from largescale networks is a challenging problem. First, there 

needs to be some metric for what constitutes a graph 

community; second, an algorithm for finding such 

communities (related solutions are NP-complete) must 

be prescribed; lastly, there must be some method of 

verifying that the computed groups are indeed meaningful. Various metrics have been proposed and several 

optimization algorithms have been introduced in the 

literature. 

The underlying question remains: how well do 

these approaches work in practice? So far, there has 

been limited work in verifying and validating the results on a wide array of application domains. The 

results of current state-of-the-art algorithms work well 

in some situations, such as when vertices clearly belong to one (and only) community, but the real world is 

not so ideal. More complicated approaches allow for 

overlapping communities, but fundamental problems 

remain. 

As an alternative approach, we have been investigating a different notion of “community” which does 

not fit previous methodologies but nonetheless provides interesting insights. Rather than being based on 

conventional graph cuts, this approach builds “cells” or 

“clusters” from the ground up by isolating low-degree 

nodes into a separate subgraph and analyzing the connectedness of resulting network. That is, given a 

degree threshold, we create a subgraph consisting of 

only nodes with that less than or equal to that degree 

value. This subgraph is largely fragmented into disconnected components, which can be useful in finding 

small, isolated fringe groups amidst the noise of largeorder hubs. 

Figure 23, for example, shows the shows the nontrivial connected components of a web network 

(http://math.nist.gov/) by restricting it to a subgraph of 

nodes with (in/out) degree 15 or less. It reveals various 

structures: e.g. ladders, star, and cluster patterns representing tightly coupled webpages. These form the 

nucleus of isolated communities, and by varying the 

degree parameter we can direct the size and granularity 

of groups revealed. This information can be used to 

augment a conventional algorithm to better identify 

small or rural communities. 

We are expanding this line of investigation by asking the question of what happens as one varies the 

degree parameter in this experiment. At a low degree 

threshold (near 1) we see a small fragmented graph of 

either isolated nodes, or individual pairs of nodes. As 

we increase this value, we include more nodes in the 

subgraph, increasing the number of communities. 

However, some of these communities also increase in 

Figure 22. P-Metric of the math.nist.gov web graph, showing 

cluster size distribution as the degree threshold varies from 0 to 

the maximum degree of the graph. The “wall” on the left illustrates the large number of leaf nodes and described the 

“bushiness” of the graph; the “hill” in the middle reveals the 

medium-sized clusters (10-100) which form good candidates for 

coarsening; the “hook” on the right reveals the formation and 

growth of the giant component.
Summary of Activities for Fiscal Year 2011 43 

size and merge with others, thus providing a contraction effect. For connected networks, as the threshold is 

increased to the maximum degree, we are left with a 

single component: the complete network graph. Thus, 

as one turns the degree-threshold parameter, the number of components (communities) starts out small, 

grows, and eventually shrinks to number of connected 

components in the original graph. 

 A more detailed analysis not only includes the component count at a given degree value, but also the size 

distribution of these components. The Profile Metric 

(or P-Metric) of a graph is the frequency distribution of 

component sizes of a degree-induced subgraph as the 

threshold value varies between 0 and the maximum 

degree of the graph; see Figure 22. This not only reveals several properties (such as the degree 

distribution, and the formation and growth of the giant 

component) but also provides a visual thumbprint of 

the graph structure, which is different from conventional community detection results. This measurement 

can be used to identify clusters for graph coarsening, or 

to reveal differences between “real” and “random” 

graphs. We are currently investigating these ideas to 

develop hybrid metrics which better describe the complex nature of these graphs. 

Figure 23. Non-trivial components of the math.nist.gov web graph, restricted to nodes with combined degree less than or equal to 15, classifying 1,380 pages into 101 groups. These form meaningful “communities” which can be useful in reducing the original graph to a coarsened 

version.
44 NIST Applied and Computational Mathematics Division 
Summary of Activities for Fiscal Year 2011 45 

Part III: Project Summaries 

 Part III 

 Project Summaries
 46 NIST Applied and Computational Mathematics Division 
Summary of Activities for Fiscal Year 2011 47 

Mathematics of Metrology 

Mathematics plays an important role in the science of metrology. Mathematical models are needed to understand how to design effective measurement systems, and to analyze the results they produce. Mathematical 

techniques are used to develop and analyze idealized models of physical phenomena to be measured, and 

mathematical algorithms are necessary to find optimal system parameters. Finally, mathematical and statistical techniques are needed to transform the resulting data into useful information. Our goal is to develop 

fundamental mathematical methods and analytical tools necessary for NIST to continue as a world-class metrology institute, and to apply them to critical measurement science applications. 

Unsuspected Nonuniqueness in 

Solving Parabolic Equations 

Backward in Time 

Alfred Carasso 

See feature article, page 29. 

Molecular Movies: Imaging 

Femtosecond Motion during 

Electrochemical Transitions 

Bradley Alpert

Joel Ullom et al. (NIST PML) 

Chris Cromer et al. (NIST PML) 

Ralph Jimenez et al. (NIST PML/JILA) 

Henry Kapteyn et al. (University of Colorado/JILA) 

Vital to the development of next-generation nanomaterials, including photovoltaics and industrial 

catalysts, is an understanding gained through measurement of electron release, transport, and transfer in 

engineered nanostructures. This project, chosen in 

2010 for a NIST Innovations in Measurement Science 

award, proposes a revolutionary, table-top x-ray imaging system to capture the motion of electrons, atoms, 

and molecules on femtosecond time scales and with 

picometer spatial resolution. 

The combination of table-top x-ray lasers, a dramatic recent breakthrough developed at JILA, with 

transition-edge sensor (TES) microcalorimeter spectroscopy, intensively developed and refined in the 

NIST Quantum Electronics and Photonics Division, 

promises to enable these new measurement capabilities. The integration of these components, 

accompanied by significant increase in detector array 

sizes, to achieve large increases in temporal and spatial 

resolution while maintaining extraordinary TES energy 

resolution, requires new data modeling and processing 

techniques. These techniques will overcome current 

limitations by 

 Resolving temporal overlap in photon detection 

while achieving energy resolution of temporally 

isolated arrivals, 

 Improving efficiency in elimination of lowfrequency background noise, and 

 Extending multiplexing and reducing cross talk in 

extracting the signals from below 1 degree Kelvin 

to room temperatures. 

Wiener filtering, long used among astronomers for 

estimating amplitudes of pulses of known shape contaminated with noise of known frequency content, is 

suitable for measuring isolated pulses. Novel processing approaches are being developed and 

characterized that rely on this knowledge but are suitable for overlapping pulses. 

This year progress occurred in the following areas: 

1. Alpert proposed a method for computing filters in 

the time domain, rather than the frequency domain, eliminating processing artifacts of the 

discrete Fourier transform, which are significant in 

this application. The motivation for the change, 

Figure 24. Pulses illustrating pile-up.
 48 NIST Applied and Computational Mathematics Division 

however, was to obtain a flexibility that allows 

imposition of filtering constraints. In particular, 

orthogonality to exponentials of one or more time 

constants enables a measured pulse energy to be 

insensitive to prior pulses. Initial tests of the new 

filters, at relatively low pulse rates, provided encouraging results [1]. Higher-rate experiments are 

being developed. 

2. A filtering method recently proposed by other researchers, which is intended for inline processing 

and trades some resolution for simplicity and ability to handle high pulse rates, was analyzed [2]. 

3. A computational tool was developed that should 

enable rapid construction of filters, “on the fly,” 

for particular pulse arrival times. The tool provides fast application to a vector of the inverse of a 

covariance matrix for stationary noise whose covariance can be expressed as a short linear 

combination of exponentials. The potential here is 

the elimination of any signal-to-noise penalty associated with the method [1] mentioned above. 

Another processing issue concerns sensor nonlinearities at higher frequencies. As the new systems are 

built and characterized, other sources of uncertainty 

will undoubtedly arise and need to be understood, and 

this broad collaboration has been assembled for this 

purpose. 

Two scenarios, one with pile-up, are shown in 

Figure 24 (top). From the pulse shape and noise autocovariance, a filter orthogonal to exponentials of two 

slow decays is computed (inset, separate vertical 

scales). Convolving the filter with the signal yields 

peaks of essentially constant height (bottom), nearly 

eliminating pile-up dependence. 

Energy resolution (i.e., uncertainty) for the 97 keV 

gamma-ray emission line of 153 Gd is shown in Figure 

25 as a function of the minimum pulse separation time, 

for two different filters. The first filter (green) is orthogonal to constants, while the second (red) is 

orthogonal to both constants and decaying exponentials 

with 6 ms time constant. The added constraint removes sensitivity to nearby pulses, while incurring 

some penalty in signal-to-noise ratio. 

[1] B. Alpert, J. Fowler, D. Bennett, R. Doriese, J. Ullom, 

A. Hoover, N. Hoteling, and M. Rabin, Improved High 

Rate Pulse Processing Algorithms for Microcalorimeters, 14th International Workshop on Low Temperature 

Detectors, August 2, 2011. 

[2] B.K. Alpert, W.B. Doriese, J.W. Fowler, J.N. Ullom, 

Predicted Energy Resolution of a Running-Sum Algorithm for Microcalorimeters, Journal of Low 

Temperature Physics (2011), doi:10.1007/s10909-011-

0441-2. 

Sparse Representations in High 

Dimensional Geometry 

Bradley Alpert 

Yu Chen (New York University) 

Laboratory and clinical diagnostic systems often produce images that lack quantitative information or 

comparability across imaging systems, which can lead 

to difficulties in diagnosis and long-term management 

of disease that requires patient monitoring. Elaborate 

measurements are taken, digitally processed, then reported in essentially qualitative form. For MRI, 

functional MRI, and some other processes, formation 

of the images relies on filtering and Fourier transformation. 

Although the computational recovery of functions 

from their Fourier representations is considered routine, aside from possible efficiency concerns arising 

from non-grid data, standard approaches assume that 

the functions are smooth and can be recovered with the 

discrete Fourier transform (computed via the FFT). 

When this assumption fails, as is evident from Fourier 

data that are not small at the highest frequencies measured, some sort of attenuation, or belling, scheme is 

typically used. This procedure tends to blur sharp features and, being more art than science, can lead to 

different functions (images) in different systems. Although this problem, and the Gibbs phenomenon, have 

received considerable attention from mathematicians in 

recent years, recently developed methods tend to work 

well only in an asymptotic sense; they do not exploit 

available data efficiently. 

Despite inherent limits on resolution that can be 

obtained from truncated Fourier data, a change of assumptions from smooth to piecewise smooth can lead 

to significantly improved recoveries. 

Procedures implementing this idea are not completely established even for functions (signals) in one 

dimension; they are yet more challenging in two and 

three dimensions, where discontinuities may be expected to occur along mostly smooth curves or 

surfaces. This constraint, which magnifies the advantage of the piecewise smoothness assumption, must 

be appropriately reflected in the methods used. Alpert 

Figure 25. 97 keV line resolution.
Summary of Activities for Fiscal Year 2011 49 

and Chen are conducting extensive numerical experiments to understand this environment and to develop 

reliable procedures for these problems. 

In recent months, understanding is developing of 

how to generate, test, and refine hypotheses regarding 

locations of discontinuities. This approach uses a spatial (i.e., physical domain) divide-and-conquer strategy 

enabled by use of prolate spheroidal wave functions in 

a statistical estimation procedure. These tools are used 

to cope with the non-convexity of the problem. As estimates are increasingly aggregated spatially, lesssupported hypotheses are eliminated and moresupported ones are refined. Once the discontinuity locations are known, recovery of the discontinuous 

function is a generally well-conditioned procedure consisting of solving a linear system of equations. 

A related, yet more general, challenge is parsimonious, or sparse, representation and recovery of 

functions under assumptions appropriate to an application. Although there is considerable current interest in 

the mathematical community in these problems (L1

-

norm minimization, compressive sensing, sparse representation in high-dimensional geometry), and much 

recent progress (initiated in pivotal work by Candes, 

Romberg, and Tao) most of the methods being explored are limited to linear spaces. While linearity is a 

natural starting point, strong evidence suggests that 

image recovery cannot be done this way yet nevertheless may be within reach. It is the goal of this project 

to develop procedures for robust recovery of piecewise 

smooth, or otherwise constrained, functions from Fourier data. 

Applied Hierarchical Control 

Anthony Kearsley 

 Optimal control problems constitute an interesting 

case of PDE-based optimization problems. Instances of 

these types of problems abound in applications, especially those in measurement science. Efficient 

numerical methods for the solution of these problems 

have been the subject of significant recent research [1], 

but recently specialized numerical methods are being 

developed for application-specific problems. 

Motivated by specific scientific and engineering 

applications, such as those arising in calibrating and 

optimizing instrument performance, we investigate a 

means of formulating a class of optimal control problems in which desired behavior of solutions or 

“targets” can be partitioned into categories of increasing relative importance. 

There is no unique mathematical formulation of 

these types of problems; indeed different formulations can generate completely different “optima” or 

solutions. In one formulation, the problem is posed as 

the minimization of a weighted sum of the deviations 

from the targets with weights corresponding to an established priority among the targets (see [7]). Another 

formulation, sometimes referred to as goal programming, insists that a set of preferred targets be satisfied 

to within certain tolerances and the others be reduced 

as much as possible within these constraints (see [5]). 

Both of these approaches involve the choice of a set of 

weights or tolerances for which there may be little theoretical guidance. 

An instance of this problem occurs, for example, 

in calibrating a MALDI/TOF mass-spectrometer when 

one knows the total amount of compound present in a 

sample, suggesting one minimizes a least squares or 

distance regression function while simultaneously maximizing signal to noise. Motivated by this application, 

and others, we seek to formulate this problem as a collection of nested optimization problems in which the 

solutions of the inner problems are determined using 

the variables in the outer problems as parameters. This 

approach is based on the work of von Stackelberg [3] 

in an economic context, requiring that the deviations 

from the least important targets, called the “follower” 

targets, be decreased only after the deviations from the 

most important targets, called the “leader” targets, satisfy prescribed bounds. This type of optimal control 

problem has been termed hierarchical control [2]. One 

way of formulating this type of problem is in terms of 

nested optimization structure in which, in an “inner 

minimization,” the follower targets are minimized subject to fixed values of certain of the control variables, 

and then an “outer minimization” is performed over the 

remaining control variables to obtain optimal leader 

target satisfaction [3]. The accuracy on the follower 

targets is therefore determined by, and is subordinate 

to, the optimization over the leader targets. In the case 

of MALDI/TOF calibration, matching known experimental parameters would be a primary objective and 

maximizing signal to noise, a secondary or “follower” 

objective. 

Recently we have derived optimality conditions 

for a linear differential equation [8] and are very close 

to extending our results to a more general reaction diffusion equation [9]. This work constitutes significant 

steps towards the ultimate goal of robustly and reproducibly optimizing instrument performance for 

multiple objectives (e.g., matching output while simultaneously maximizing signal to noise). 

[1] R. Glowinski, J.L. Lions and J. He, Exact and Approximate Controllability for Distributed Parameter Systems: 

A Numerical Approach, Cambridge University Press, 

2008. 

[2] J.L. Lions, Hierarchical Control, Proceedings of the 

Indian Academy of Sciences (Mathematical Sciences)

104 (1) (Feb. 1994), pp. 295–304. 
 50 NIST Applied and Computational Mathematics Division 

[3] L. Vicente and P. Calamai, Bilevel and Multilevel Programming: A Bibliography Review, Journal of Global 

Optimization 6 (1994), pp. 1–16. 

[4] H. von Stackelberg. Marktform und Gleichgewich, J. 

Springer, Vienna, 1934. 

[5] J.P. Ignizio, Goal Programming, Lexington Books, Lexington Massachusetts, 1976. 

[6] J. Koski, H. Eschenaur and A. Osycka, Multicriteria 

Design Optimization, Springer-Verlag, Berlin, 1990. 

[7] A.J. Kearsley, Optimality Conditions for the Hierarchical Control of a Linear Partial Differential Equation, 

in Proceedings of the 2nd IEEE Conference on Instrumentation, Control and Automation, November 2011. 

[8] A.J. Kearsley, Hierarchical Control of a Reaction Diffusion Equation, International Journal on Applied 

Mathematics and Statistics, Special Issue on Instrumentation, Control and Automation, to appear.

Denoising Helium Ion Microscope 

Nanoscale Imagery

Alfred Carasso 

Andras Vladar (NIST PML) 

Helium Ion Microscope (HIM) images are particularly 

rich in surface morphological detail, but are generally 

quite noisy. A major challenge is to denoise these images while preserving delicate surface information. A 

NIST-invented technology, based on smoothing HIM 

images g(x, y) by applying a fractional diffusion equation, 

w ( ) w, t 0, w(.,0) g(x, y) t       , 

with fixed β such that 0.1 ≤ β ≤ 0.2, has been found 

very useful. In that method, ║׏g║1, the L1

 norm of the 

gradient of the noisy HIM image, is first evaluated. A 

value of λ, with 0 < λ < 1 is then prescribed, and the 

forward solution of the diffusion equation is terminated 

at the earliest time t

†

 where 

1 1 w(.,t)   g

FFT algorithms are used to solve the fractional diffusion equation. By visually monitoring the evolution up 

to time t

†

, a user can decide whether too much or too 

little smoothing has occurred. One can then backtrack 

to an earlier image, or restart the procedure with a new 

value of λ. Values of λ ≈ 0.3 have been found useful 

for many HIM images at NIST. 

Considerable work has been published on other 

denoising methods. One of the best-known is the total 

variation (TV) method, which assumes the true noiseless image to be of bounded variation and defines the 

TV denoised image by means of 

}. 2 ( , ) Argmin { 2

( ) 1 2

tv g x y 2 u u g u BV R     



The minimization needed to produce gtv can best be 

accomplished by one of two methods: applying the 

Split Bregman iteration, or computing the long time 

steady-state solution to the nonlinear Marquina-Osher 

second order parabolic equation, with the noisy image 

g(x, y) as initial data. Here, in contrast to the fractional 

diffusion method, there is no a-priori user control on 

the gradient of gtv, and consequently, 

1 1

tv g  g

typically. This characteristic feature of TV denoising 

has been found detrimental in NIST applications to 

HIM imagery. Indeed, as noted below, the fundamental 

reason why TV denoising is not helpful is because 

HIM and SEM images are not of bounded variation. 

Lipschitz exponent analysis. Many natural images 

f(x,y) are not smoothly differentiable functions of x and 

y, but involve non-differentiable localized fine structures and texture, in addition to edges. The L1

 Lipschitz 

exponent α, where 0 < α ≤ 1 is a mathematical index 

that can be used to estimate image fine structure content. Images that are of bounded variation or smoother 

have α=1. The value of α decreases with increasing 

fine structure. A patented NIST-developed methodology, based on FFT algorithms, can be used to evaluate 

image Lipschitz exponents. Typical SEM or HIM images have Lipschitz exponents α < 0.6, and are not of 

bounded variation. TV denoising forces gtv(x,y) ∈

BV(R2

), which often leads to smoothing out of texture 

and/or elimination of localized fine scale information. 

A typical example is shown in Figure 1 and confirmed 

in Table 1. The fractional diffusion image maintains 

fidelity to the surface morphology of the sample, as is 

evident from the jagged edges and foreground surface 

texture. These important elements are not wellrecovered in the TV image. Fractional diffusion reduces ║׏g║1 by a prescribed factor of 3, while conserving 

║g║1, leading to a denoised Lip α = 0.451. In contrast 

TV denoising falsely reduces ║g║1 by 16%, reduces 

║׏g║1 by a factor of 7 or more, and leads to a significantly higher denoised Lip α = 0.751. 

Quantitative validation of fractional diffusion denoising. A research project of considerable interest to 

the NIST Mechanical Metrology Division involves 

artificially generated SEM and HIM nanoscale images, 

obtained by using a sophisticated computer program 

developed in PML. This program can generate physically realistic degraded images that mimic very 

precisely the characteristics of modern nanoscale instrumentation. The amount and type of noise can be 

controlled, as well as the amount and type of blur. Because the true image is known, such realistic degraded 

imagery can be used to evaluate the performance of 
Summary of Activities for Fiscal Year 2011 51 

various image processing methodologies. Fractional 

diffusion denoising was applied to five artificially generated SEM and HIM images, with increasing levels of 

noise-induced degradations. Excellent results were 

found when comparing the denoised images with the 

true images, with noise being reduced by quite significant amounts ranging from 35 to 46 percent. 

Equivalent short time smoothing using other evolution equations. An obvious advantage of the fractional 

diffusion method is the ability to terminate the process 

at the exit time t

†

, the earliest time at which ║g║1 has 

been reduced by the prescribed amount. A natural 

question is whether similar useful denoising can be 

obtained with more standard evolution equations, by 

exiting at the same prescribed value of ║g║1. Two 

natural candidates are the linear isotropic heat conduction equation, and the nonlinear anisotropic MarquinaOsher equation. This topic is currently being explored. 

Uncertainty Quantification in 

Scientific Computing 

Andrew Dienstfrey 

Ronald Boisvert 

http://www.nist.gov/itl/math/ifip-woco-10.cfm 

ACMD hosted the Working Conference on Uncertainty 

Quantification in Scientific Computing in Boulder, CO 

on August 1-4, 2011. The 76 participants representing 

10 countries were a unique mix of mathematicians, 

statisticians, computer scientists, application scientists 

and managers who gathered together to consider the 

role of metrology in mathematical modeling and computer simulation. Such techniques and tools 

increasingly are playing critical roles as adjuncts to, or 

replacements for, direct physical measurement in both 

product design and societal decision making. 

The program was divided into four theme areas: 

(1) Uncertainty Quantification Need: Risk, Policy and 

Decision Making, (2) Uncertainty Quantification Theory, (3) Uncertainty Quantification Tools, and (4) 

Uncertainty Quantification Practice. Keynote addresses 

 After 0.2 Frac diffusion denoising After Split Bregman TV denoising 

 

Figure 26. TV denoising retains less fidelity to surface morphology than does fractional diffusion denoising, leading to a higher Lipschitz 

exponent.

Table 1. 

Image g(x, y) ║g║1 ║׏g║1 Lip α

Noisy HIM original (600 nm) 88 25000 0.231 

After Frac diffusion (β = 0.2, t

† = 0.1) 88 8500 0.451 

After Split Bregman TV (ω = 0.025) 74 3400 0.751 
 52 NIST Applied and Computational Mathematics Division 

were delivered by Pasky Pascual of the US Environmental Protection Agency, Michael Goldstein of 

Durham University (UK), William Kahan of the University of California at Berkeley, Scott Ferson of 

Applied Biomathematics, and Maurice Cox of the National Physical Laboratory (UK). A panel discussion 

featured Sandy Landsberg of the DOE Office of Science, Larry Winter, former Deputy Director of the 

National Center for Atmospheric Research, and 

Charles Romine of NIST. Antonio Possolo, Chief of 

ITL’s Statistical Engineering Division, and Mark Cunningham of the US Nuclear Regulatory Commission, 

were also notable plenary speakers. 

The participants represented a wide variety of applications, including cosmology, weather/climate 

modeling, remote sensing/atmospheric chemistry, hydrology, nuclear energy/safety, fluid dynamics, 

engineering mechanics, manufacturing processes, medicine, toxicology, and computer security. 

The meeting was organized by Andrew Dienstfrey 

and Ronald Boisvert of ACMD as part of ITL’s Virtual 

Measurements Program. It was co-sponsored by the 

International Federation for Information Processing 

(IFIP) Working Group 2.5 on Numerical Software. The 

proceedings, currently under development, will be published by Springer. 

ITL Program: Virtual Measurement Systems

Virtual Measurements in Quantum 

Chemistry 

Raghu Kacker 

Rüdiger Kessel 

Russell Johnson (NIST MML) 

Karl Irikura (NIST MML) 

By a virtual measurement we mean a prediction along 

with its associated uncertainty for the value of a measurand determined from a computational model as an 

alternative to a physical measurement. An important 

application is quantum chemistry, where carefully determined uncertainties have not been reported. As the 

technology improves, the need and importance of determining reliable uncertainties in virtual 

measurements is being recognized. This project is focused on developing and applying methods for 

quantifying the uncertainty associated with a virtual 

measurement in quantum chemistry. The benefits accrue to research and development of chemical 

processes, materials development, and drug discovery. 

Predictions from computational quantum chemistry models seldom agree with the corresponding highquality physical measurements. The differences are 

not random but systematic. Therefore, a common practice is to apply an empirical scaling factor to computacomputational predictions to bring them closer to the 

true measured values. The empirical scaling factor carries uncertainty. We have developed a methodology to 

quantify the uncertainty associated with a scaling factor. This approach is based on the Guide to the 

Expression of Uncertainty in Measurement [1], which 

is an international standard. The uncertainties for scaling factors lead to the corresponding uncertainties for 

virtual predictions. 

Our 2005 paper on uncertainties in the scaling factors for ab initio vibrational frequencies [2] has been 

cited 132 times. This indicates that scientific community has started paying attention to uncertainties in the 

outputs of computational models. 

Recently, the Journal of Chemical Physics received a critique of our 2009 paper “Uncertainties in 

scaling factors for ab initio vibrational zero-point energies” and of another paper like ours. Our response, 

appearing in the Journal of Chemical Physics [3], 

points out that the problem addressed in the critique is 

different than the problem which we addressed. An 

independent response submitted to the same journal 

reached the same conclusion. 

In 2010 we had reported scaling factors and uncertainties separately for low and high vibrational 

anharmonic frequencies. Anharmonic frequencies are 

calculated from higher order models and require considerably more computational effort. However, our 

continuing investigations indicate that the scaling factors are not substantially improved relative to lower 

order harmonic vibrational frequencies. This leads to 

questions about the benefits of higher order anharmonic frequencies. 

[1] Evaluation of Measurement Data --- Guide to the Expression of Uncertainty in Measurement, JCGM 100, 

Joint Committee for Guides in Metrology, (2008). 

[2] K. K. Irikura, R. D. Johnson III, R. N. Kacker, Uncertainties in Scaling Factors for ab Initio Vibrational 

Frequencies, Journal of Physical Chemistry A 109 

(2005), pp. 8430-8437. 

[3] R.D. Johnson III, K.K. Irikura, R. Kacker, and R. Kessel, Response to “Comment on ‘Uncertainty in scaling 

factors for ab initio vibrational zero-point energies’ and 

‘Calibration sets and the accuracy of vibrational scaling 

factors: A case study with the X3LYP hybrid functional,’” Journal of Chemical Physics 134 (2011), article 

167102. 

ITL Program: Virtual Measurement Systems
Summary of Activities for Fiscal Year 2011 53 

Bubble Motion and Size Variation 

during Thermal Migration with 

Phase Change 

Asha Nurse 

Geoffrey McFadden 

Sam Coriell (NIST MML)

If a temperature gradient is applied to a liquid containing gas bubbles, the bubbles can occasionally be 

observed to migrate in the direction of higher temperatures; this effect can even overcome the usual 

buoyancy forces on the bubble. The source of such 

bubble motion is often the so-called Marangoni force 

that arises due to the temperature dependence of the 

gas-liquid surface energy. A thermally-induced variation of surface energy tangential to the interface gives 

rise to lateral stresses that drag fluid from the hotter 

regions to colder regions; the resulting flow tends to 

translate the drop into hotter regions. 

 The general study of surface effects such as the Marangoni force is important in many materials 

processing applications, where a parent phase is transformed into a daughter phase. If the parent and 

daughter phases are both fluids, then the effects of fluid 

flow in general, and Marangoni flow in particular, can 

have an important effect on the quality of the processed 

material. Steve Hardy, a NIST material scientist, conducted a series of experiments studying the motion of 

an air bubble in silicone oil under carefully controlled 

thermal conditions [1]. By comparing with theoretical 

predictions of bubble velocity versus temperature gradient, he was able to measure the temperature 

dependence of the surface energy, which is a quantity 

of fundamental interest in this field. 

To interpret his experiments Hardy used the theory 

of drop migration developed by Young, Goldstein, and 

Block in 1959 [2]. They obtained an expression for the 

steady velocity of a fluid drop contained in an immiscible liquid with a vertical temperature gradient. The 

velocity depends on the drop radius, the applied temperature gradient, the gravitational acceleration, and 

various material properties, and represents the interplay 

of the Marangoni force and the buoyancy force on the 

bubble. In particular they predict the possibility of stationary drops when these forces exactly balance; in that 

case there is a linear relation between drop radius and 

the applied temperature gradient. 

In many cases Hardy observed that the bubble did 

not translate at a uniform rate, but instead moved up 

and down on a vertical trajectory while the radius of 

the drop also oscillated periodically in time; an example is shown in Figure 27. His measurements were 

made at the limits of the motion where the bubble reverses direction, and at these points he applied the 

corresponding results of Young et al. for the stationary 

bubble. Hardy’s explanation for the observed oscillatory behavior was based on the exchange of air between 

the bubble and the liquid. The solubility of air in the 

liquid phase depends on temperature, and the liquid 

may be super-saturated with air in its hotter regions and 

under-saturated in the colder regions. In hot regions the 

diffusion of gas from the liquid into the bubble causes 

the radius to increase, and also causes the buoyancy 

force to increase so that the bubble rises. In the cooler 

region the opposite occurs, leading to the oscillatory 

behavior.

We have extended the theory of Young et al. to 

consider the case of a drop that can grow or shrink in 

time, and move with a non-uniform velocity. In our 

preliminary work the drop is assumed to be the vapor 

phase of the corresponding liquid. The change in phase 

as the drop grows or translates can give rise to a density-driven flow through the interface as well as local 

heating due to the latent heat release at the interface; 

these effects are absent in the treatment of Young et al. 

By solving the coupled Navier-Stokes equation and 

heat equation for the two-phase system in a quasi-static 

limit we derive first order nonlinear ordinary differential equations for the time dependence of the bubble 

radius and the position of the center of the bubble. In 

certain limits we recover the results of Young et al., but 

in other regimes we obtain more complicated predictions. In particular, our equations permit a stationary 

steady state whose stability can be studied by a linear 

analysis in terms of normal modes. Under some conditions we find an oscillatory instability whose evolution 

to finite amplitude leads to transient behavior similar to 

that observed by Hardy. We also find that the effects of 

latent heat can overwhelm the Marangoni force, leading to motion in which the velocity is predicted to be a 

balance between latent heat release and buoyancy. This 

Figure 27. The vertical position Z(t) of an air bubble and diameter 

D(t) in silicone oil with a vertical temperature gradient of about 

110 K/cm plotted as a function of time t. (From S. Hardy [1]).
 54 NIST Applied and Computational Mathematics Division 

work was presented at the 2011 Annual Meeting of the 

APS Division of Fluid Dynamics [3]. 

[1] S.C. Hardy, The Motion of Bubbles in a Vertical Temperature Gradient, Journal of Colloid and Interface 

Science 69 (1979), pp. 157-162. 

[2] N.O. Young, J.S. Goldstein, and M.I. Block, The Motion of Bubbles in a Vertical Temperature Gradient, 

Journal of Fluid Mechanics 6 (1959), pp. 350-356. 

[3] A. Nurse, G. McFadden, and S. Coriell, Bubble Motion 

and Size Variation during Thermal Migration with 

Phase Change, 64th Annual Meeting of the APS Division of Fluid Dynamics, Baltimore, MD, November 20-

22, 2011.

Shape and Stability of Rotating 

Toroidal Drops 

Asha Nurse 

Geoffrey McFadden 

Sam Coriell (NIST MML)

Recently it has been shown that cells can self-assemble 

into microtissues, a process relevant to tissue engineering. The forces that drive such assembly are an area of 

intense current interest. In [1] this process was studied 

for tissue assembly on a patterned substrate consisting 

of multiple wells that each contains a conical post, 

which leads the cell to acquire a toroidal geometry as 

the tissue accommodates the post. Surface forces that 

would otherwise promote a spherical shape tend to 

cause the toroid to contract inwards, and are balanced 

by the contact forces on the post. In some instances the 

toroidal shapes are observed to develop a type of fluting instability in the azimuthal direction, reminiscent of 

the capillary-driven Rayleigh instability of a cylindrical 

column of fluid. In the present project we examine 

such instabilities in a simpler setting in which the restoring forces provided by the post are replaced by the 

centrifugal forces experienced by a rotating fluid drop, 

which tends to fling the fluid outwards. We derive the 

shapes of axisymmetric toroidal drops that minimize an 

appropriate energy functional depending on surface 

energy and rotational energy, and determine their stability by examining the second variation of the energy 

functional. 

The shape and stability of rotating spheroidal 

drops was studied by the blind experimenter J.A.F. 

Plateau in the 19th century [2]. Plateau was interested in 

the analogous problem that arises for rotating, selfgravitating celestial bodies, and realized that small 

scale experiments were possible by replacing the gravitational force by the force of surface tension, which 

also tends to consolidate the fluid. He observed that if 

the rotational forces are strong enough spheroidal drops 

elongate at the equator and contract at the poles, eventually leading to a pinch-off at the axis of rotation to 

form toroidal shapes. The spheroidal problem was 

studied theoretically by Brown and Scriven [3], who 

performed finite element computations of the deformed 

shapes based on variational principles, and by Chandrasekhar [4] who included the effects of fluid flow 

inside the drop by using a method of moments. 

We have extended the previous work by examining the transition from spheroidal to toroidal 

axisymmetric rotating drops, as illustrated in Figure 28. 

We have computed numerical solutions for the shapes 

in terms of an angle-arclength formulation, which involves the numerical solution of a two-point boundary 

value problem for nonlinear ordinary differential equations. These ODEs are the Euler-Lagrange equations 

for the energy functional, which includes both kinetic 

and potential energies from the rotation and capillarity. 

The stability of these solutions is then obtained by a 

diagonalization of the associated second variation, 

which is solved as an eigenvalue problem for the system of ODEs. Our angle-arclength formulation allows 

us to examine a larger range of parameters than Brown 

and Scriven, who were limited to single-valued spheroidal shapes by their use of a spherical coordinate 

system. Our findings include an additional instability to 

5-lobed shapes with increasing rotation rate for the 

spheroidal solutions. We have also found numerous 

instabilities on the toroidal solution branch for both 

axisymmetric and non-axisymmetric perturbations. In 

addition we find a new solution branch of prolate spheroids in the case of a lighter drop (bubble) in a heavier 

fluid medium. In this case, the shapes become elongated at the poles and contract along the equator, in 

contrast to the oblate shapes that result from rotation of 

a heavier drop within a lighter fluid. 

Figure 28. Axisymmetric liquid drops for various rotation rates; 

only the upper half of the shapes are shown. On the left are three 

oblate spheroidal shapes that develop a pronounced dimple on the 

axis of symmetry as the rotation rate increases. On the right are 

toroidal shapes that branch from the spheroidal family with further 

changes in the rotational rate.
Summary of Activities for Fiscal Year 2011 55 

[1] J. Youssef, A. K. Nurse, L. B. Freund, and J. R. Morgana, Quantification of the Forces Driving Self-assembly 

of Three-dimensional Microtissues, Proceedings of the 

National Academy of Sciences 108 (2011), pp. 6993–

6998. 

[2] J. A. F. Plateau, Experimental and Theoretical Researches on the Figures of Equilibrium of a Liquid Mass 

Withdrawn from the Action of Gravity, Annual Report 

of the Board of Regents of the Smithsonian Institution

(1863), pp. 270-285, Washington, D.C. 

[3] R. A. Brown and L. E. Scriven, The Shape and Stability 

of Rotating Liquid Drops, Proceedings of the Royal Society of London A 371 (1980), pp. 331-357. 

[4] S. Chandrasekhar, The stability of a rotating liquid drop, 

Proceedings of the Royal Society of London A 286 

(1965), pp. 1-26.

Boundary Slip Effect on the Stability 

of Spiral Poiseuille Flow 

Geoffrey B. McFadden 

David L. Cotrell (CD-adapco, Bellevue, WA) 

P. Aaron Lott (Lawrence Livermore National Lab) 

Advances in micro-fabrication techniques have provided significant understanding into the behavior of fluids 

at small scales. Small-scale experiments, with flow 

driven by pressure gradients, drainage, shear, or an 

electric field have reported a breakdown of the no- slip 

boundary condition, with observed slip lengths as large 

as microns. In addition, numerical studies of fluids are 

often performed with no-slip boundary conditions, and 

the effects of introducing slip as a model of surface 

roughness is of current interest. 

We consider the effect boundary slip has on the 

stability of spiral Poiseuille flow, which is an annular 

flow with an applied pressure gradient. This flow provides a good test-bed for stability studies, as it 

combines the effects of axial pressure gradients and 

centripetal acceleration associated with curved boundaries. We find that under certain conditions slip has a 

significant effect on the linear stability of the flow. 

Numerical results indicate that linear stability is sensitive to the ratio between the inner and outer cylinder 

radii, as well as the slip length. Changes in these parameters cause the flow to be stabilized or destabilized 

in reference to a flow where no-slip conditions are applied; this change in stability is indicated by change in 

critical Taylor number. The dependence of stability on 

radius ratio becomes more complicated as the Reynolds 

number is increased; in particular, the flow becomes 

destabilized by small ratios, stabilized by mid-range 

ratios and de-stabilized again for large ratios. We have 

computed estimates of the critical radius ratios where 

slip has no effect on the stability of the flow. The results have been submitted for publication [1]. 

[1] D.L. Cotrell, P.A. Lott and G.B. McFadden, Boundary 

Slip Effects on the Stability of Spiral Poiseuille Flow, 

submitted.

A Multicomponent and Multiphase 

Model of Reactive Wetting 

Geoffrey B. McFadden 

William J. Boettinger (NIST MML) 

James A. Warren (NIST MML) 

W. Villanueva (Royal Inst. of Technology, Sweden) 

Reactive wetting occurs when a liquid and substrate 

can interact chemically; for example, the substrate may 

dissolve in the liquid, or the liquid may diffuse into the 

substrate. In this case the understanding of the wetting 

process involves not only capillary considerations but 

also the thermodynamics of the components and their 

tendency to combine in order to minimize the free energy of the system. These effects result in a more 

complicated process, since the substrate plays an active, rather than a passive, role in establishing the 

system geometry, including the determination of free 

surfaces and contact angles. 

An interesting aspect of wetting concerns the dynamics associated with the motion of the contact lines 

at the junction of the liquid, solid, and vapor phases. 

For the simpler problem of spreading on an inert planar 

substrate, it is well known that the imposition of standard no-slip boundary conditions at the moving contact 

line leads to a non-physical singularity in the flow field 

at the contact line. To alleviate this effect we introduce 

a diffuse interface description of the inter-phase 

boundaries, which also tends to relieve the hydrodynamic singularity. In the case of reactive wetting, 

another mechanism for dissipation is the diffusion of 

solute near the contact line, which introduces possible 

non-equilibrium effects in the dynamical description of 

the motion. 

The mechanisms of reactive wetting thus involve 

the interplay of fluid flow, heat and mass transport, 

capillary phenomena, and phase transformations. We 

have recently developed a mathematical model of reactive wetting in an isothermal, three-component, fourphase system. To treat free surfaces and contact lines in 

the problem, a diffuse interface, or phase field, model 

is used, which involves the introduction of additional 

order parameters that track the local phase at each point 

and incorporate the effects of capillarity and interfacial 

adsorption of solute. A manuscript describing the work 

has been completed, and is currently under internal 

review prior to submission for publication. 

[1] W. Villanueva, W.J. Boettinger, G.B. McFadden, and 

J.A. Warren, A Multicomponent and Multiphase Model 

of Reactive Wetting, submitted.
 56 NIST Applied and Computational Mathematics Division 

Measurement of the Flow Stress of 

Carbon Steel for High-Speed 

Machining Simulations 

Timothy Burns 

Steven Mates (NIST MML) 

Richard Rhorer (NIST EL) 

Eric Whitenton (NIST EL) 

Debasis Basak (Orbital Sciences Corporation) 

In a high-speed machining operation on a carbon steel 

such as AISI 1045, a small region (see Figure 29) of 

thickness on the order of magnitude of 10 μm is deformed plastically in the primary shear zone at a strain 

rate of the order of magnitude of 10,000 s-1, to a true 

strain on the order of 100%, on a time interval on the 

order of 10 microseconds. Subsequently, the material is 

subjected to additional large plastic strain in the secondary shear zone, for a time that is typically less than 

1 millisecond. During this very short cutting time, the 

work material is sheared so rapidly that it undergoes an 

increase in temperature of the order of magnitude of 

1000 oC (see Figure 30). Thus, plastic working by rapid 

shear in these two thin material regions induces a heating rate on the order of magnitude of one million 

degrees Celsius per second. Under such extreme dynamic loading conditions, there is insufficient time for 

thermally-activated processes that take place on significantly longer time scales to cause significant changes 

in the material’s microstructure. On the other hand, 

unique non-equilibrium superheated microstructural 

states can be present during high-speed machining operations. As a result, the material flow stress in a highspeed machining process can differ significantly from 

that which is measured experimentally under equilibrium high-temperature conditions. This presents unique 

difficulties for both experimental measurement and 

constitutive response modeling of the flow stress in 

these materials for use in finite-element simulations of 

high-speed machining processes. The NIST PulseHeated Kolsky Bar Laboratory has been developed to 

obtain improved constitutive response data under conditions of rapid heating for application to machining 

studies, as well as for other applications. 

Following our discovery using the NIST Kolsky 

Bar that AISI 1075 steel exhibits a nonequilibrium 

phase transition under conditions of rapid heating and 

very short time at high temperature [1], we reviewed 

our experimental data on AISI 1045 steel. The AISI 

1045 was also found to exhibit a nonequilibrium phase 

transformation at high strain rate, which is similar to 

the one we had observed to take place in AISI 1075 

steel [2]. An interesting feature of both of these data 

sets is that the material has a stiffer response to compressive loading when it has been preheated using 

pulse-heating to a testing temperature that is below the 

eutectoid temperature, than it does when it has been 

preheated using a slower heating method. On the other 

hand, in both cases, when the material has been pulseheated to a temperature that exceeds the eutectoid temperature prior to compressive loading on the Kolsky 

bar, it is shown to exhibit a significant loss of strength. 

A consequence of this behavior is that fixed-parameter 

constitutive models, such as the well-known JohnsonCook model, which is frequently used in finite-element 

simulations of high-strain-rate deformation processes, 

cannot be used to describe this constitutive response 

behavior. This may help to explain, at least in part, why 

sophisticated, state of the art finite-element software 

gives poor temperature predictions in computer simulations of high-speed machining processes on carbon 

steels of interest in manufacturing, such as AISI 1045. 

[1] T.J. Burns, S. P. Mates, R.L. Rhorer, E.P. Whitenton, 

and D. Basak, Dynamic Properties for Modeling and 

Simulation of Machining: Effect of Pearlite to Austenite 

Phase Transition on Flow Stress in AISI 1075 Steel, 

Machining Science & Technology 15 (2011), pp. 1–20. 

[2] T.J. Burns, S.P. Mates, R.L. Rhorer, E.P. Whitenton, D. 

Basak, Effect on Flow Stress of a Rapid Phase Transition in AISI 1045 Steel, in Proceedings of the ASME 

Figure 29. Schematic drawing of two-dimensional orthogonal 

cutting operation, showing primary and secondary shear zones. 

Figure 30. False-color thermal image of high-speed, steadystate orthogonal machining of AISI 1045 steel; taken from [3].
Summary of Activities for Fiscal Year 2011 57 

2011 International Manufacturing Science and Engineering Conference, Corvallis, Oregon, June 13-17, 

2011. 

[3] M.A. Davies, H. Yoon, T.L. Schmitz, T.J. Burns, and 

M.D. Kennedy, Calibrated Thermal Microscopy of the 

Tool-chip Interface in Machining, Machining Science & 

Technology 7 (2003), pp. 166-190.

Modeling the Temperature on the 

Tool-Chip Interface during HighSpeed Machining 

Timothy Burns 

Steven Mates (NIST MML) 

Richard Rhorer (NIST EL) 

Eric Whitenton (NIST EL) 

Debasis Basak (Orbital Sciences Corp.) 

During high-speed machining of many materials, very 

high temperatures are generated along the tool-chip 

interface. In a simplified planar orthogonal cutting 

model that is still widely used in the literature (see Figure 31), the workpiece material enters a thin cutting 

region called the primary shear zone at temperature θ0, 

where it is deformed by rapid plastic shearing, and is 

heated to a much higher temperature, θs. The bulk of 

the heat generated in the primary shear zone is rapidly 

convected away from the workpiece, along with the 

chip of removed material is that is being formed. Some 

of this heat is also conducted into the tool and into the 

workpiece material. The material continues to deform 

and rapidly increase in temperature as it moves up the 

face of the tool, under conditions of large frictional 

forces, in a region called the secondary shear zone. 

Experimental measurements indicate that the maximum 

temperature, θm, occurs along the interface between the 

chip and the tool, near the region where the chip begins 

to curl away and lose contact with the tool. There is 

also a large transfer of heat away from this secondary 

deformation zone, mainly by convection along with the 

chip, but also by conduction. This high temperature 

environment can cause rapid tool wear. Thus, there is 

considerable interest in obtaining an estimate of the 

peak temperature, θm, under realistic cutting conditions. 

Peak temperature predictions using state of the art 

finite-element (FEM) software have been found to underestimate the temperature in orthogonal cutting of 

AISI 1045 steel by as much as 33%. There are two 

likely reasons for this poor predictive capability. The 

first is that the forces used in the simulations, which are 

computed using the workpiece material flow stress 

constitutive model that is used in the FEM software, 

are not modeled accurately. The second is that the 

models used to simulate the friction along the tool-chip 

interface are inadequate. Our current work [1] involves 

using experimental measurements, obtained using the 

NIST Kolsky bar, of the stress strain response of AISI 

1045 steel, along with a friction model that is more 

sophisticated than the usual Coulomb sliding friction 

model that is used in the FEM software, to achieve 

improved peak temperature predictions of some experimentally measured orthogonal cutting tests. These 

predictions are obtained using a two-dimensional singularly-perturbed convection-diffusion model for the 

temperature distribution that is based on a number of 

cutting temperature models in the machining literature. 

[1] T. J. Burns, S. P. Mates, R. L. Rhorer, E. P. Whitenton, 

and D. Basak, On Modeling the Peak Temperature on 

the Tool-chip Interface during High-speed Machining of 

AISI 1045 Steel, submitted. 

Simulation of Bioregulatory 

Networks Involved in Cell Cycle 

Control 

Geoffrey B. McFadden 

Mirit Aladjem (National Institutes of Health) 

S. Kim (National Institutes of Health) 

Kurt Kohn (National Institutes of Health) 

A. Luna (NIH and Boston University) 

G. McFadden is a co-advisor to Sohyoung Kim, a postdoctoral fellow, and Augustin Luna, a graduate student 

from Boston University, who are both doing research at 

the National Institutes of Health (NIH); their coadvisors are NIH researchers M. Aladjem and K. Kohn. 

The team is developing models of bioregulatory networks that are involved in cell cycle control. The 

Figure 31. Schematic drawing of orthogonal cutting process. The 

first region of large heat generation during high-speed machining 

is in the primary shear zone, indicated in red, and the second 

region of large heat generation is in the secondary shear zone 

along the tool- material contact region of length L, indicated in 

purple.
 58 NIST Applied and Computational Mathematics Division 

models consist of systems of nonlinear ordinary differential equations that typically exhibit switching 

behavior, limit cycles, and other types of bifurcations. 

Proper cell growth depends on a network of interacting 

molecules that monitors cellular metabolism and environmental signals. This network ensures that cells halt 

their growth in response to unfavorable conditions such 

as the absence of sufficient nutrients or the presence of 

potentially damaging agents. When cells escape these 

controls, the results are developmental abnormalities, 

genomic instability, and cancer. 

Much current work by Sohyoung Kim focuses on a 

protein known as p53, a tumor suppressor that causes 

cell cycle arrest or programmed cell death in response 

to stress signals such as DNA damage. Regulating the 

appropriate levels of p53 is essential for cell survival. 

Two associated proteins, Mdm2 and Mdmx, are known 

regulators of p53. Mdm2 can facilitate degradation of 

p53, whereas the mechanism of the regulatory interaction of Mdmx with p53 is not clear. It is also not 

obvious how those three proteins will operate together 

under various conditions. To address those questions a 

mathematical model has been developed [1] to investigate the interactions of these three proteins by 

numerical simulations. The modeling work has suggested experimental investigations of the role of Mdmx 

in the cell cycle that are currently being performed by 

Dr. Kim at the Laboratory for Molecular Pharmacology 

at the NIH National Cancer Institute. 

Recent work by Augustin Luna includes the development of models for the role played by a protein, 

SIRT1, in regulating cellular response to DNA damage. 

Resveratol, naturally found in red wine and linked with 

extended lifespans in rodents, stimulates the gene that 

produces SIRT1. This work is modeling the effects of 

SIRT1 on the mammalian circadian clock cycle. It is 

known that the time of day that cancer treatments are 

administered affects drug efficacy, and circadian 

rhythms are also known to affect DNA damage response. SIRT1 is known to play a role in the DNA 

damage sensor that triggers the cellular response to 

genotoxic stress. In this work existing models for the 

circadian clock are being modified to include the specific effects of SIRT1 on the interaction between the 

DNA damage response and the circadian cycle in cells. 

A poster describing this work was presented at a recent 

international conference on systems biology [2]. G. 

McFadden is serving on A. Luna’s Ph.D. thesis committee at Boston University. 

[1] S. Kim, M.I. Aladjem, G.B. McFadden, and K.W. Kohn, 

Predicted Functions of MdmX in Fine-tuning the response of p53 to DNA damage, PLoS Computational 

Biology 6 (2010), article e1000665 (18 pages). 

[2] A. Luna, G. McFadden, M. Aladjem, and K. Kohn, A 

Computational Mammalian Circadian Clock Model with 

Connections to the DNA Damage Response, 12th International Conference on Systems Biology, Heidelberg, 

Germany, August 28 - September 1, 2011. 

Mathematical Optimization of 

Procedures for Cryoprotectant 

Equilibration 

James D. Benson 

Anthony J. Kearsley 

Adam Z. Higgins (Oregon State University) 

Stabilization of viable cells by cryopreservation is important in several areas, including cell-based therapy, 

tissue engineering and transplantation medicine. Cryopreservation nearly universally depends on the 

equilibration of cells and tissues with high concentrations of permeating chemicals known as cryoprotective 

agents, or CPAs. Despite their protective properties, 

CPAs can cause damage as a result of osmoticallydriven cell volume changes, as well as chemical toxicity. In this study, we have used previously published 

data to determine a toxicity cost function, a quantity 

that represents the cumulative damage caused by toxicity. We then used this cost function to define and 

numerically solve the optimal control problem for CPA 

equilibration, using human oocytes as representative 

cell type with high clinical relevance. The resulting 

toxicity-optimal procedures are predicted to yield significantly less toxicity than conventional stepwise 

procedures. In particular, our results show that toxicity 

is minimized during CPA addition by inducing the cell 

to swell to its maximum tolerable volume and then 

loading it with CPA while in the swollen state. This 

counterintuitive result is considerably different from 

the conventional stepwise strategy, which involves 

exposure to successively higher CPA concentrations in 

order to avoid excessive shrinkage. The procedures 

identified in the present study have the potential to 

significantly reduce damage due to toxicity. A manuscript describing this work is currently under review. 

[1] J. Benson, A. J. Kearsley, and A. Z. Higgins, Mathematical Optimization of Procedures for Cryoprotectant 

Equilibriation Using a Toxicity Cost Function, Cryobiology, accepted. 
Summary of Activities for Fiscal Year 2011 59 

A Standard Candle for Extragalactic 

Metrology 

Bert W. Rust 

Type Ia supernova are so luminous at peak brightness, 

with lightcurves so uniform and regular, that they 

promise to be excellent standard candles for measuring 

distances to their parent galaxies. To use them for this 

purpose, it will be necessary to calibrate their luminosities by observing detailed light curves of several 

supernovae in nearby galaxies whose distances can be 

reliably estimated by more conventional methods. These distances can then be used to give good estimates of 

the absolute luminosities of the supernovae, which can 

then be compared to the observed luminosities of more 

distant supernovae to get estimates of their distances. 

It has long been known [1] that the late time decline of the light curve is powered by the nuclear decay 

chain 56Ni → 56Co → 56Fe, with the two decay rates 

accelerated by a common factor, presumably because 

the decays take place in the interiors of white dwarf 

stars. The deposition and subsequent decay of the 56Ni 

can be modeled by 

( ) Ni Co Fe 56 56 56 1 2 k kW t   

where W(t) is a three-parameter Weibull probability 

density function, i.e., 































   













 

 

3  2

3

1

( 1)

3

1

3

2

1 2 3

exp

( ) ( ; , , )

 













  

t t

W t W t

with adjustable parameters, α1, the time that 56Ni deposition begins, α2, a shape parameter, and α3, a scale 

parameter. The decay rates are well modeled by 

, 0 1, 111.42

1 , 8.764

1

4

4

2

4

1    

 

k k

where 8.764 d and 111.42 d are the terrestrial half-lives 

of 56Ni and 56Co, respectively, and the adjustable parameter α4 specifies the amount by which these halflives are shortened by the ambient temperature and 

density in the white dwarf. If N1(t), N2(t), and N3(t) are 

the relative abundances of 56Ni, 56Co, and 56Fe, then 

, ( ) 0,

, ( ) 0,

( ) , ( ) 0,

2 2 3 1

3

1 1 2 2 2 1

2

1 1 1 1

1

 

  

  







k N N

dt

dN

k N k N N

dt

dN

W t k N N

dt

dN

Assuming that the ratio of the energy releases from the 

56Ni and 56Co decays is the same as that observed in a 

terrestrial setting, i.e., 3.67 MeV / 1.71 MeV = 2.146, 

the observed luminosity can be modeled by 

( ) ( )  ( ) 2.146 ( ), 1 2 1 1 2 2 L t  C W t C k N t  k N t

where C1 and C2 are adjustable parameters which convert fluxes into relative luminosities. Thus the model 

has six free parameters, four nonlinear and two linear. 

Figure 32 shows the result when it is fitted to the observations for supernova SN1990N. The fit explains 

99.91% of the total variance in the measurements! 

The ratio of the estimates C1

 and C2

 and 

their standard uncertainties, i.e., 

5.0156 0.228

( )

( )

2 2

1 1  





C C

C C  

 



 , 

provides a means to estimate the energy per nucleon 

produced by the 56Ni deposition process: 

E(

56Ni depos.)/nucleon = 8.577 ± .390MeV. 

Since the binding energy per nucleon for the 56Ni nucleus, 8.790 MeV, lies well inside the 1σ interval, the 

above results are consistent with the hypothesis that the 

deposition of 56Ni is accomplished by the fusion of 56 

protons. 

[1] B.W. Rust, M. Leventhal and S.L. McCall, Evidence for 

a radioactive decay hypothesis for supernova luminosity,

Nature 262 (1976) pp. 118-120. 

Figure 32. The light curve of SN1990N in relative luminosity units. 

The time variable is measured in Julian Day units. The discrete data 

points are the observed luminosities and the smooth curve is the 

model fit.
 60 NIST Applied and Computational Mathematics Division 

Unfolding Optical Spectrum Measurements 

Bert W. Rust 

Dianne P. O’Leary 

Stephen W. Brown (NIST PML) 

We have begun a consulting effort with Steven W. 

Brown of the NIST Optical Technology Division (685) 

on correcting optical spectrum measurements for scattered light in a spectrometer. Figure 34 shows (in cyan) 

the spectrum measured for a lamp used as a calibration 

source. The black curve is a crude first approximation 

to the corrected spectrum. The gaps in the black curve 

represent wavelength intervals in which the correction 

process gave negative values, a physical impossibility. 

The object of the current effort is to compute statistical 

confidence interval bounds for the corrected spectrum, 

to compare them with first approximations like the one 

shown in the Figure, and to develop alternate methods 

for computing the corrected spectra. 

In order to do a proper job of unfolding the measured spectra, it is necessary to determine an instrument 

response function. As a start toward this objective we 

have been given 54 measured line spread functions 

(LSF) corresponding to 54 distinct non-equally-spaced 

wavelengths λL in the range 220.0000–859.9250 nm. 

For each of these wavelengths, the corresponding LSF 

is measured at 1024 equally-spaced wavelengths λ in 

the range 198.9388–873.9835 nm. The 54 measured 

1024-vectors are plotted in Figure 33. This 1024 × 54 

matrix must be expanded, by interpolation, into a 1024 

× 1024 matrix A. This means that we must find, on 

average, about 19 new functions in each gap between 

every pair of measured ones. The resulting matrix A

can then be used in a discrete approximation to an integral equation 

198.9388 873.9835,

( ) ( , ) ( ) ( ),

859.920

220.0000

 

  



f  A   L x  L d L  

where f(λ) is a measured spectrum to be corrected, ε(λ) 

is the measurement error in f(λ), x(λL) is the unknown 

corrected spectrum, and A(λ,λL) is the instrument response function. 

Let the discretized integral equation be written 

f  Ax   , 

where A is the required 1024 ×1024 matrix and ε is an 

unknown random 1024-vector satisfying 

(0, )

2   N S , 

where S2 is the positive definite covariance matrix for 

the measurement errors. We are currently in the process of retrieving estimates of this matrix for all five of 

the calibration sources in the study. These matrices are 

vitally important for computing estimates x

 of the corrected spectra and in computing confidence intervals 

for those estimates. Those confidence intervals will be 

computed using the BRAKET-LS algorithm. We have 

already tested that procedure using a very crude first 

approximation to S2

. To compute a complete set of 

1024 upper and lower bounds required over 40 hours 

on the Sun server “entity.” So it will not be practical to 

compute confidence intervals for every measured spectrum, but it is important to compute them for all of the 

calibration sources. 

Figure 34. The spectrum measured for a lamp used as a 

calibration source (cyan) and a crude first approximation to 

the corrected spectrum (black).

Figure 33. The measured LSF functions. 
Summary of Activities for Fiscal Year 2011 61 

Variable Projection for Nonlinear 

Least Squares Problems 

Dianne P. O’Leary 

Bert Rust 

Fitting a model to measured data provides the most 

basic tool in science and engineering, essential to discovering and analyzing patterns and causality. 

Software that accomplishes this task should be both 

efficient and robust, providing reliable estimates of the 

model’s parameters in a reasonable amount of time. 

Yet data fitting problems are often quite challenging numerically. In fitting exponential models, for 

example, small changes in the data can make large 

changes in the optimal parameters. Equally serious is 

the fact that data fitting problems are most often nonconvex, so a set of parameters can be optimal among 

nearby sets of parameters without being globally optimal, and software can be fooled into accepting a 

suboptimal solution. 

We focus in this work on fitting nonlinear models 

in a (weighted) least squares sense. Most nonlinear 

models have some parameters – perhaps quite a few – 

that appear linearly. For example, in fitting a sum of 

two exponentials, the model for the data observations 

y(t1), . . . , y(tm) might be 

 ( ) ( , , ) 1 2

1 2 y t c e c e η t t t    α c   . (1) 

The parameters c = [c1, c2]

T

 appear linearly, so for every choice of nonlinear parameters α = [α1, α2]

T

, optimal 

values for c can be found by solving a linear leastsquares problem, a rather simple computational task. 

How can this be used to our advantage? Consider the 

nonlinear least-squares problem 

 2

2 min y η(α,c) α,c

 , (2) 

where the ith component of the vector y is the observed 

value y(ti), and the ith component of the vector η is the 

model prediction at ti (i =1, . . . ,m). Then the solution 

to (2) is the same as the solution to 

 2

2 min y η(α,c(α)) α

 , (3) 

where η(α, c(α)) denotes the model predictions when, 

given α, we determine the parameter values c optimally. 

This simple observation was made and exploited 

in 1973 by Gene Golub and Victor Pereyra [1]. They 

called (2) a separable least squares problem and proposed solving it using the variable projection algorithm 

(3). In 1974, Fred Krogh [2] discussed some implementation issues and noted that this approach solved 

problems for which the standard nonlinear least squares 

algorithm failed. The variable projection algorithm was 

implemented in a very widely-used software module 

called varpro, written in 1977 in Fortran by John 

Bolstad [3], using ideas of Linda Kaufman [4] to speed 

up the computation of derivatives. This code is also 

distinguished as being the first least squares code produced by the numerical analysis community that 

included computation of the covariance matrix, which 

provides the foundation for the statistical analysis of 

the estimate. The history and wide range of applications of varpro are summarized in [5]. The beauty of 

variable projection is that it reduces the number of parameters in the minimization problem, thus improving 

efficiency and possibly reducing the number of local 

minimizers. Convergence to the globally optimal solution is therefore more likely. Implementation of the 

idea is rather complicated, though, since the Jacobian 

matrix for (3) must be derived from that for (2). 

Inevitably, the 1977 varpro program is showing 

its age. In particular, the thousand-line program relies 

on 1970s technology for overcoming the limitations of 

static storage allocation, and it uses an outdated implementation of a minimization algorithm. The purpose 

of our work is to provide a 21st century sample implementation of the variable projection method (in 

Matlab) that allows a more general formulation (with 

constraints on the parameters), more clearly identifies 

its key ingredients so that improvements can be made, 

computes the Jacobian matrix more accurately, and 

makes future implementations in other languages easy. 

Our Matlab implementation contains over 400 lines of 

comments for fewer than 160 lines of code [6]. It also 

has the advantage that it returns extensive statistical 

diagnostics that are extremely important not only for 

validating the model, but also in changing the model 

when it is shown to be inadequate. 

[1] G. H. Golub and V. Pereyra, The Differentiation of 

Pseudoinverses and Nonlinear Least Squares Problems 

whose Variables Separate. SIAM Journal on Numerical 

Analysis 10 (1973), pp. 413–432. 

[2] Fred T. Krogh, Efficient Implementation of a Variable 

Projection Algorithm for Nonlinear Least Squares Problems. Communications of the ACM 17 (March 1974), 

pp. 167–169. 

[3] John Bolstad, VARPRO computer program, January 

1977. Computer Science Department, Serra House, 

Stanford University. 

[4] L. Kaufman, A variable projection method for solving 

separable nonlinear least squares problems. BIT Numerical Mathematics 15 (1975), pp. 49–57. 

[5] G. H. Golub and V. Pereyra, Separable nonlinear least 

squares: The variable projection method and its applications. Inverse Problems 19 (2003), pp. 1–26. 

[6] D. P. O’Leary and B. W. Rust, Variable Projection for 

Nonlinear Least Squares, submitted. 
 62 NIST Applied and Computational Mathematics Division 

Shape Analysis 

Javier Bernal 

Charles Hagwood (NIST ITL) 

John Elliott (NIST MML) 

Michael Halter (NIST MML) 

The recognition and classification of objects in observed images is an important goal in image analysis. 

For this purpose the analysis of shapes of objects in 

images has become an important tool. Accordingly 

biomedical image analysis is a major application of 

shape analysis. In particular biomedical images that 

show cells responding to stimuli are good candidates 

for shape analysis. This is because change in shape is a 

known response of a cell to stimuli. 

Work is currently under way for the development 

of a framework based on differential geometry for formulating mathematical representations of shape and for 

performing calculus with these representations. In this 

framework shapes will be treated as points in a differential manifold with a Riemannian metric and tools for 

computing geodesic distances between points will be 

readily available. 

[1] C. Hagwood, J. Bernal, M. Halter, and J. Elliott, Evaluation of Segmentation Algorithms on Cell Populations 

Using CDF Curves, IEEE Transactions on Medical Imaging, accepted. 

Neural Networks 

Javier Bernal

A backpropagation algorithm is being implemented for 

training neural networks to be used for the identification of subcellular features in cell images relevant to 

cell biologists. Approaches exist for recognizing objects or pattern classes associated with an image based 

on the use of sample patterns (training patterns) to estimate statistical parameters of each pattern class. 

However the statistical properties of the pattern classes 

might not be known or might be difficult to estimate. 

Therefore a method such as the neural network approach that produces the required decision functions 

based solely on training without assumptions about 

probability density functions associated with the pattern classes may be more successful at handling the 

problem. 

 A neural network is a computational model that 

consists of computing elements called “neurons” organized as a network reminiscent of the way in which 

neurons are believed to be interconnected in the brain. 

It is an adaptive system that changes its structure based 

on information that flows through the network during a 

training phase. It is mostly used for modeling relationships between input and output data and for partitionpartitioning data into classes. 

During the training with the backpropagation algorithm the average squared error between the network's 

output and a target value is minimized for each point or 

pattern (in d-dimensional space) in the training set. 

Via training, coefficients of decision functions are obtained and associated with neurons in the network. 

Once the training is done other data points or patterns 

are put through the network and assigned to a class 

according to the output obtained. For our purposes the 

resulting implementation will be used for identifying 

pattern classes in d-dimensional space as each pixel in 

an image is associated with a d-dimensional pattern, 

the coordinates of the pattern corresponding to d distinct attributes associated with the pixel. 

Since learning in a neural network is equivalent to 

minimizing an error function of several variables 

(weights in the network), the Conjugate Gradient 

Method (CGM) has been implemented. Two tasks remain to be completed: 

i. Implementation of a “model trust region” method for correcting the situation in which the error 

function is not quadratic enough around the current weights for the CGM to work, a situation 

that occurs when the Hessian of the error function is not positive definite or when the current 

weights are not close enough to the optimal solution. 

ii. Implementation of a probabilistic heuristic (e. g., 

simulated annealing) for correcting the situation 

in which the CGM gets stuck at a local minimum that is not a global optimum. 
Summary of Activities for Fiscal Year 2011 63 

High Performance Computing and Visualization 

Computational capability is advancing rapidly. This means that modeling and simulation can be done with 

greatly increased fidelity (e.g. higher resolution, more complex physics). However, developing large-scale 

parallel applications remains highly challenging, requiring expertise that application scientists rarely have 

In addition, the hardware landscape is changing rapidly, so new algorithmic techniques must constantly be 

developed. We are developing and applying facilities and expertise of this type for application to NIST problems. Large scale computations and laboratory experiments invariably produce large volumes of scientific 

data, which cannot be readily comprehended without some form of visual analysis. We are developing the infrastructure necessary for advanced visualization of scientific data, including the use of 3D immersive 

environments and applying this to NIST problems. One of our goals is to develop the 3D immersive environment into a true interactive measurement laboratory. 

Rheology of Dense Suspensions 

John Hagedorn 

Steven Satterfield 

Marc Olano 

Judith Terrill 

Nicos Martys, Edward Garboczi (NIST EL) 

Pascal Hebraud (CNRS/ESPCI, France) 

See feature article, page 34. 

Segmentation and Tracking of 

Breast Cancer Cells 

Adele Peskin 

D.J. Hoeppner (National Institutes of Health) 

C.H. Stuelten (National Institutes of Health) 

See feature article, page 38. 

Body Area Network Visualization 

and Analysis 

John Hagedorn 

Judith Terrill 

Kamran Sayrafian-Pour (NIST ITL) 

Wen-Bin Yang (NIST ITL) 

Kamya Yekeh Yazdandoost (University of Oulu) 

Attaphongse Taparugssanagorn (University of Oulu) 

Matti Hämäläinen (University of Oulu, Finland) 

Jari Iinatti (University of Oulu, Finland) 

See feature article, page 32. 

ITL Program: Pervasive Information Technology 

Modeling, Visualization of Cement 

Paste Hydration and Microstructure 

Development 

William George 

Steven Satterfield 

Judith Terrill 

Jean-Loup Traore 

Jeffrey Bullard (NIST EL) 

Edward Garboczi (NIST EL) 

Paul E. Stutzman (NIST EL) 

http://www.nist.gov/itl/math/hpcvg/hydrationhpc.cfm 

http://www.nist.gov/itl/math/hpcvg/hydrationvis.cfm 

When cement powder is mixed with water, the 

hydration process that transforms the paste from a fluid 

suspension into a hardened solid involves complex 

chemical and microstructural changes. Understanding 

and predicting the rates of these changes is a 

longstanding goal. Computational modeling of the 

hydration of cement is challenging because it involves 

a large number of coupled nonlinear rate equations that 

must be solved in a highly irregular three-dimensional 

spatial domain. To address these challenges we are 

applying a new computational model called 

HydratiCA, which has several advantages. HydratiCA 

uses stochastic cellular automaton algorithms to 

simultaneously model 3-D reaction and transport 

phenomena. This allows us to track the detailed 

kinetics and equilibria that occur in a diverse range of 

cementious systems. 

Parallelization of the model is important so that we 

can simulate systems that are large enough to be 

realistic, avoiding finite size effects, and still be able to 

complete the simulations in a reasonable amount of 

time. Visualization of the output is important both for 

validation and to understand the results. Over the 

course of the simulation time, a series of data volumes 

is produced at the time values of interest. 
 64 NIST Applied and Computational Mathematics Division 

Our paper describing the modeling [1] was 

selected as one of the top 10 highlights of the journal 

Modeling and Simulation in Materials Science and 

Engineering for 201013. 

 This year we implemented the creation and 

coalescence of void space in the simulation. Cement 

hydration reactions conserve mass, but generally result 

in reduced volume of condensed matter (liquid or 

solid). The computational domain has a fixed volume 

throughout the simulation, so it is necessary to handle 

the reduction in total condensed volume as a simulation 

proceeds. We modified the program to create a bubble 

object in the largest open pore space and then grow the 

size of the bubble with time. We contributed to a paper 

on using supercomputers [2] as well as a keynote 

presentation at a major international cement chemistry 

meeting [3]. We also completed a computational and 

quantitative visualization study of the C3S-gypsum 

 

13 http://iopscience.iop.org/0965-

0393/page/Highlights%20of%202010

system [4] (see Figure 35). In the coming year, we plan 

to use quantitative visualization to study new cases. 

[1] J.W. Bullard, E. Enjolras, W.L. George, S G. Satterfield, 

and J.E. Terrill, A Parallel Reaction-Transport Model 

Applied to Cement Hydration and Microstructure 

Development, Modelling and Simulation in Materials 

Science and Engineering 18 (2) (March 2010), article 

025007 (16 pages).

[2] J.W. Bullard, E.J. Garboczi, W. L. George, N.S. Martys, 

S.G. Satterfield, J.E. Terrill, Advancing the Materials 

Science of Concrete with Supercomputers, Concrete 

International 33 (1) (Jan. 2011), pp. 24-29. 

[3] J. W. Bullard, N. S. Martys, J.-L. Traore, W. L. George, 

S. G. Satterfield, Computer Models as Guides Through 

Material Design Space, International Congress on the 

Chemistry of Cement, Madrid, Spain, July 3-8, 2011. 

[4] L. Valentini, J. W. Bullard, G. Artioli, J. Traore, J.E. 

Terrill, Role of Sulfate Incorporation into C-S-H during 

Cement Hydration: Results from Numerical Modeling of 

the System, C3S-gypsum, submitted. 

Figure 35. This is a visualization of a simulation of the hydration of tricalcium silicate (C3S) in water. The blue particles are C3S, a soluble 

mineral which is the majority component of Portland cement concrete. The yellow glyphs indicate areas where the primary hydration product 

phase, calcium silicate gel, nucleates and grows on the C3S particle surfaces. The graph shows the time dependence of the concentration of 

calcium and silicate ions in solution, illustrating the level of quantitative detail that can be extracted from the simulations. 
Summary of Activities for Fiscal Year 2011 65 

Measuring Errors in Polygonal Representations of Surfaces 

John Hagedorn 

Marc Olano 

Judith Terrill 

http://www.nist.gov/itl/math/hpcvg/psurferr.cfm

Surfaces are important objects of study in widely diverse scientific disciplines and the depiction of surfaces 

and interactions with surfaces are important tasks in 

scientific visualization. In this context, we often (indeed, typically) work with surface models that are 

approximations of the true surfaces that they represent. 

When the representations of surfaces are used to make 

decisions or to make quantitative assessments of properties of the underlying surfaces, it is critical to 

understand the errors inherent in the representations. 

The most common way of approximating surfaces is 

with sets of polygons. In this project we have developed quantitative metrics for assessing how well these 

polygonal representations portray the underlying surfaces. 

We look at three types of errors in polygonized 

surfaces: distance, surface area, and volume. For distance errors, we start with the simple idea of looking at 

a point on the polygonal representation and seeing how 

far away from the true surface that point lies. We can 

then assess the error over the entire surface by integrating this distance error over the surface. Surface area 

and volume errors are much simpler to assess. For 

surface area, we simply sum the areas of the polygons 

in the polygonal representation and compare with the 

true surface area of the underlying surface. Similarly, 

for closed polygonal representations, we can easily 

calculate the enclosed volume, which can be compared 

with the analytically determined volume of the underlying surface. 

We have implemented these error metrics in software and tested them on a variety of quadric surfaces. 

We polygonized each surface in several ways, either 

directly from the analytic definition of the surface or by 

creating a gridded data set and generating a polygonal 

isosurface. The isosurface polygonizations are intended (in some way) to emulate an experimental situation, 

and in that vein we added various levels of noise to the 

gridded data sets. We note that these methods can be 

applied to any surface type and any polygonization. 

For each surface and each polygonization scheme, 

we tested polygonizations at progressively finer scales. 

The finer polygonizations have more polygons and are 

expected to more closely approximate the surfaces. 

The results of our tests enable us to quantify the errors 

of these polygonal representations relative to the underlying true surfaces. Furthermore, we see clear 

relationships between the measured errors and the 

number of triangles in a given approximation. These 

relationships can be modeled with simple formulas. 

For example, Figure 36 shows a scatterplot of our normalized mean distance error metric versus the number 

of triangles for each of four polygonization schemes 

for our tests of elliptic paraboloids. This plot also 

shows the curves that we have fit to the data. 

Unlike the other statistics, the surface area error 

metric does not appear to tend to zero as the number of 

triangles increase for isosurface polygonizations in the 

presence of noise. By analyzing the marching cubes 

isosurface polygonization algorithm we were able to 

explain this limit behavior. The limits predicted by our 

mathematical analysis correspond closely to those calculated by fitting the error data. 

Qualitatively our results are entirely expected; for 

example, coarser polygonizations have greater error. 

But these methods enable us to measure and quantify 

this qualitative understanding. This quantitative understanding of error is critical as we apply other 

quantitative methods to these polygonal approximations of surfaces. 

[1] J. Hagedorn, M. Olano, J. Terrill, Measuring Errors in 

Polygonal Representations of Surfaces, submitted. 

ITL Program: Virtual Measurement Systems

Figure 36. Scatterplot of normalized mean distance error versus 

number of triangles for all polygonizations of the elliptic paraboloids. Data for each of the four polygonization schemes has been 

fitted and the resulting lines plotted.
 66 NIST Applied and Computational Mathematics Division 

Processing Large Phantom Image 

Sets 

Adele Peskin 

Alden Dima (NIST ITL) 

Ganesh Saiprasad (NIST ITL) 

http://www.nist.gov/itl/math/hpcvg/medimgvis.cfm 

A large number of image sets of artificial lungs with 

tumors (“phantoms”) are available from the FDA to 

serve as ground truth for the assessment of 

measurements of lung tumor properties [1]. 

Anthropomorphic phantom data can be set up and 

scanned repeatedly across many different sites to 

compare imaging equipment and tumor volume 

measurements. Figure 38 shows the FDA phantom 

lung, into which sets of phantom tumors consisting of 

materials of known density are placed, and a sample 

resulting slice of CT data. CT scans of the data yield 

spots of predictable pixels intensities, corresponding to 

the density of the tumors that are inserted. In order to 

use the CT data for volumetric comparisons, the exact 

locations of tumors in each data set are needed. These 

can be extracted manually, but this is an extremely time 

consuming job. We are creating a processing tool to 

extract the location of each tumor in these sets, and 

then calculate a tumor volume, based on our biweight 

volumetric measurement algorithm [2]. 

 The main challenge of extracting the tumors in the 

lung data is to separate them from the lung walls and 

from surrounding blood vessels, both of which have 

similar densities, and so resulting CT data will contain 

pixel intensities in the same range. We currently have 

an algorithm that will isolate most of the tumors from 

these sets. An example is shown in Figure 37. The 

algorithm involves separating the inside from the 

outside of the lung in each slice of data, finding 

clusters of pixels with intensities in the range of the 

tumor, and then eroding and dilating to separate the 

tumors from surrounding structures. Resulting pixel 

clusters are then chosen as tumors according to their 

geometry and their size. 

 Currently we are working on improving our 

algorithm to process the thousands of data sets 

available from the FDA efficiently. This work includes 

improving our location of the lung wall, more accurate 

tumor geometry selection, and removal of pieces of 

blood vessels from the tumors according to the pixel 

distributions inside the pixel clusters that represent the 

blood vessels. 

 This work will also provide the foundation for a 

more generalized problem of locating lung tumors in 

clinical data, a much harder problem. In clinical data, 

the tumor geometries are unknown, and blood vessels 

attachments can be more complicated, as are the ways 

in which clinical tumors attach to the lung wall. Small 

tumors are the most challenging, often not providing 

enough pixel data to detect a peak in a histogram of the 

pixel distribution in the area of the tumor. However, 

automated location of tumors in large sets of clinical 

Figure 37. A sample lung data set, shown with an iso-surface of -

100 Hounsfield units, to display the lung tumors, lung walls, and 

sections of blood vessels. To the right the corresponding extracted 

tumors are displayed at the same locations.

 

 Figure 38. FDA lung phantom (left), and sample CT slice containing a phantom tumor (right).
Summary of Activities for Fiscal Year 2011 67 

data would be a powerful tool in disease detection and 

in monitoring tumor growth over time. 

[1] https://wiki.nci.nih.gov/display/CIP/Phantom+FDA

[2] A. Peskin, K. Kafadar, A. Dima, J. Bernal and D. 

Gilsinn, Synthetic Lung Tumor Data Sets for 

Comparison of Volumetric Algorithms, in Proceedings 

of the 2009 International Conference on Image 

Processing, Computer Vision, and Pattern Recognition, 

Las Vegas, NV, July 13-16, 2009. 

Visualizing Fire and the Resulting 

Deformation of Structures 

Terence Griffin 

Greg Rami 

Dennis Backhaus 

Marc Olano 

Kevin Harrison 

Judith Terrill 

Dilip Banerjee (NIST EL) 

John Gross (NIST EL) 

http://www.nist.gov/itl/math/hpcvg/firedeformvis.cfm

We are collaborating with researchers in the NIST Engineering Laboratory (EL) to study the effects of fire 

on building structures in order to improve structural 

engineering and building safety. We are using a sequential process in which the EL Fire Dynamics 

Simulator (FDS) is used to simulate the start and propagation of fire in a room, after which a second code 

(finite element heat transfer analysis) calculates how 

heat computed by FDS diffuses into structural members. A third program (finite element analysis) takes 

the output of the second code and computes how the 

structure deforms over time due to combined effects of 

thermal and mechanical loads. After specifying a scenario, we run the three simulations followed by our 

software to automatically create the geometry of the 

building, our software to specify crack patterns in windows, and our software (based upon the Bullet Physic 

Engine) for the dynamics of the shards in breaking 

glass windows. Then, we link the fire, thermal, structural data, and any window dynamics with a separate 

real-time visualization capability that can be run on the 

desktop and in the NIST 3D immersive environment. 

This enables interactive measurement and analysis of 

the resulting data. 

This year we wrote a 3D room navigator that 

works by clicking on rooms in a displayed map. This 

enables real-time visualization and analysis in multistory multi-room buildings. We enhanced our software 

to create the dynamics of broken glass shards; see Figure 39. We developed a tool to automate the layout of a 

building (floors, rooms) and included the capability to 

specify beam types. We completed the automation of 

the process to create a demo, and added enhanced 

analysis tools. In the coming year, we will be studying 

new building structures. 

Nano-structures, Nano-optics, and 

How to Squeeze the Light out of 

Quantum Dots 

James S. Sims 

John Kelso 

Garnett W. Bryant (NIST PML) 

http://www.nist.gov/itl/math/hpcvg/nanohpc.cfm

http://www.nist.gov/itl/math/hpcvg/nanovis.cfm

Research and development of nanotechnology, with 

applications ranging from smart materials to quantum 

computation to biolabs on a chip, has the highest national priority. Semiconductor nanoparticles, also 

known as nanocrystals and quantum dots (Qds), are 

one of the most intensely studied nanotechnology paradigms. Nanoparticles are typically 1 nm to 10 nm in 

size, with a thousand to a million atoms. Precise control of particle size, shape and composition allows one 

to tailor charge distributions and control quantum effects to tailor properties completely different from the 

bulk and from small clusters. As a result of enhanced 

quantum confinement effects, nanoparticles act as artificial, man-made atoms with discrete electronic spectra 

that can be exploited as light sources for novel enhanced lasers, discrete components in nanoelectronics, 

qubits for quantum information processing, and enhanced ultrastable fluorescent labels for biosensors to 

detect, for example, cancers, malaria or other pathogens, and to do cell biology. 

In a joint project with the NIST Physical Measurement Lab we are developing computationally 

efficient large scale simulations of such nanostructures, 

and we are also developing immersive visualization 

techniques and tools to enable analysis of highly comFigure 39. Single frame showing glass window breaking in FireStructure simulation.
 68 NIST Applied and Computational Mathematics Division 

plex computational results of this type. The electrical 

and optical properties of semiconductor nanocrystals 

and quantum dots are studied. In the most complex 

structures this entails modeling structures with on the 

order of a million atoms. Highly parallel computational 

and visualization platforms are critical for obtaining the 

computational speeds necessary for a systematic, comprehensive study. Often it is easy to define the simple 

subsystems that make up a complex, heterogeneous 

nanosystem [1]. However, it may be difficult to explicitly define the entire structure. A novel feature of the 

code being developed is the ability to link together 

heterogeneous nanostructures. 

This year the work was focused on modulating and 

controlling the optical properties of self-assembled 

quantum dots using external strain [2], and using electric fields [3]. Calculations were carried out on NIST's 

4,404-processor Linux cluster. 

To understand how applied stress can be used to 

actively control dot optical properties, dots buried at 

different points in a nanobridge oscillator or cantilever 

have been considered. The dependence of the dot’s 

electronic states and optical transitions on the coupling 

to bending modes of the oscillator has been studied. 

The dependence on applied stress can be understood as 

a competition between the internal and external stress 

that can affect the local strain at the dot. As the computational model has been extended to handle more 

complex and larger systems by including not only the 

nanostructures but also the substrate and environment 

around them, parallel processing has become even 

more of a necessity. Both shared memory OpenMP 

parallelization and distributed memory MPI are employed. 

Future work will add the effect of external magnetic fields into the tight-binding diagonalization tool and 

to expand the atomic orbital basis to include the effect 

of d orbitals. 

[1] G.W. Bryant and W. Jaskolski, Electronic Properties of 

Quantum-dot Molecules, Physica E 17 (2003), pp. 40-

41. 

[2] G.W. Bryant, M. Zieliński, N. Malkova, J. Sims, W. 

Jaskólski, and J. Aizpurua, Effect of Mechanical Strain 

on the Optical Properties of Quantum Dots: Controlling 

Exciton Shape, Orientation, and Phase with a Mechanical Strain, Physical Review Letters 105, article 067404 

(2010). 

[3] G.W. Bryant, N. Malkova, J. Sims, M. Zielinski, W. 

Jaskolski, and J. Aizpurua, Controlling the Optics of 

Quantum Dots with Nanomechanical Strain, Physical 

Review B: Condensed Matter and Materials Physics, accepted. 

3D in Web Pages 

Sandy Ressler 

Halley Coplin 

John Hagedorn 

Kamran Sayrafian (ITL) 

http://www.nist.gov/itl/math/hpcvg/3dweb.cfm 

It is now possible to embed 3D computer graphics into 

web pages such that the 3D graphics are “first class 

citizens.” A recent effort led by FraunhofferGesellschaft and the Web3D Consortium has produced 

a set of tools, called X3DOM [1], for “3D declarative 

markup” that works with most modern web browsers. 

The result is the ability to put 3D graphics, generated 

using a variety of techniques, seamlessly into web pages. This 3D markup can be queried and manipulated in 

exactly the same way as document elements, such as 

paragraphs, headings, and fonts can be manipulated for 

textual components of a page. For example, one can 

query all “spheres” and change their color or scale. 

Seeking to move the technology in the standards 

arena, Sandy Ressler is participating in the W3C Declarative 3D Community Working Group. In addition, 

he has produced some exemplars that demonstrate the 

practicality of these techniques, and has developed 

some software [2] to ease integration of 3D models 

with web pages. 

Another example of the value of declarative 3D is 

the work of SURF student Halley Coplin. In this collaboration with Kamran Sayrafian and John Hagedorn, 

we introduced motion to the humans in the “Modeling 

RF Propagation within the Human Body” project [3]. 

This resulted in successfully animating the human geometry (surface only, not organs); see Figure 40. 

Figure 40. Single Frame in an animation sequence of a human.
Summary of Activities for Fiscal Year 2011 69 

Viewers to the web site [4] can see the animations live 

on the web page and customize various aspects of the 

animation. 

In the coming year we anticipate enhancing the 

graphics of the DLMF project [5] via X3DOM. A 

number of functional controls (direction of animation, 

surface selection, navigation type) have already been 

implemented. This approach has the potential to open 

up DLMF graphics to more compute platforms (e.g., 

Linux) than currently exist [6]. 

[1] Fraunhofer, http://www.x3dom.org/. 

[2] S. Ressler, Integrating jQuery with the 3D Descriptive 

Markup of X3DOM, NISTIR 7827, October 2011. 

[3] K. Sayrafian, http://www.nist.gov/healthcare/emerging/ 

rfpropagation.cfm, 2011. 

[4] H. Coplin, S. Ressler, J. Hagedorn, RF Propagation 

Body, http://math.nist.gov/~SRessler/RF/walk50.xhtml

[5] Digital Library of Mathematical Functions. 2011. National Institute of Standards and Technology, 

http://dlmf.nist.gov/. 

[6] S. Ressler, http://math.nist.gov/~SRessler/x3dom/ 

dlmf/AIanim.xhtml

Information Visualization 

Sandy Ressler

http://www.nist.gov/itl/math/hpcvg/infovis.cfm

Information Visualization (InfoVis) is a type of visualization that focuses on non-physical data. For example 

the results of a search, the configuration of a network, 

and stock market prices are all the type of data that can 

be visualized using InfoVis techniques. Scientific visualization generally represents physical entities such as 

maps, weather, medical organs and data associated 

directly with physical objects. Our work in InfoVis has 

focused on a particular experiment concerning congestion control of networks and the resources consumed 

by a simulation of a cloud computing scenario [1]. 

 Figure 41, produced by Ressler, is a single frame of 

an animation that displays how six different variables 

representing resources used in the cloud computing 

simulation are consumed [2]. The x axis represents 100 

clusters, and the y axis represents 1000 nodes in those 

clusters, for each variable. 

In observing the animations the researchers a) 

were able to confirm that the simulation was functioning as expected ,and b) observed some unknown phephenomenon concerning resource utilization was also 

present posing questions for future research. The animations were produced using a collection of R scripts 

[3] developed for this project. 

In addition the project has also produced a simple 

hand computed demonstration of a visualization of the 

Common Vulnerability Scoring System (V2) [4,5]. 

Computing vulnerabilities are given a score based on 

the criteria of the CVSS-V2 specification. We plan on 

developing additional visualizations of computing security data in the forthcoming year. 

 In the coming year we anticipate performing several 

more visualizations focused on the cloud computing 

simulation project that is ongoing. Subsequent to this a 

collection of tools will be assembled with the goal of 

enabling the production of InfoVis simpler and faster 

in order to have impact on the research problems being 

addressed. 

[1] K. Mills, J. Filliben, D. Cho, E. Schwartz and D. Genin, 

Study of Proposed Internet Congestion Control Mechanisms, NIST Special Publication 500-282, May 2010, 

534 pages. 

[2] S. Ressler, Visualizing Cloud Computing Simulations, 

http://math.nist.gov/~SRessler/cloudviz.html

[3] R Development Core Team (2003). R: A Language and 

Environment for Statistical Computing. R Foundation 

for Statistical Computing, Vienna, Austria. 

[4] S. Ressler, http://math.nist.gov/~SRessler/nvdvis/ 

nvd_cvssv2.html

[5] P. Mell, K. Scarfone, and S. Romanosky, CVSS A 

Complete Guide to the Common Vulnerability Scoring 

System Version 2.0, June 2007, 

http://www.first.org/cvss/cvss-guide.html

ITL Program: Complex Systems

Figure 41. Single frame of an animation displaying how six variables representing resources used in the cloud computing 

simulation are consumed. The x axis represents 100 clusters, and 

the Y axis 1000 nodes in those clusters, for each variable.
 70 NIST Applied and Computational Mathematics Division 

Scientific Software

Modern science and engineering in general, and modern measurement science in particular require a wide 

variety of software tools for scientific discovery, exploration, and analysis. As scientific inquiry becomes 

deeper and more specialized, so must the supporting software tools. The goal of this work is to develop critical software tools that support measurement science at NIST, as well as computational science and 

engineering at large.

hp-Adaptive Finite Element Methods 

William F. Mitchell 

Marjorie McClain 

See feature article, page 27. 

OOF: Finite Element Analysis of 

Material Microstructures 

Stephen A. Langer 

Valerie R. Coffman 

Andrew C.E. Reid (NIST MML) 

Günay Doğan (Theiss Research) 

http://www.ctcms.nist.gov/oof/

The OOF Project, a collaboration between ACMD and 

MML, is developing software tools for analyzing real 

material microstructure. The microstructure of a material is the (usually) complex ensemble of 

polycrystalline grains, second phases, cracks, pores, 

and other features occurring on length scales large 

compared to atomic sizes. The goal of OOF is to use 

data from a micrograph of a real or simulated material 

to compute the macroscopic behavior of the material 

via finite element analysis. OOF is intended to be a 

general tool, applicable to a wide variety of microstructures in a wide variety of physical situations. 

OOF is currently being used in research at industrial, academia, and government laboratories and as a 

teaching tool in universities. Including all available 

versions, OOF2 was downloaded 1,314 times this year, 

a 20% decrease from last year. The on-line version, 

available at Purdue's nanoHUB site for computational 

materials science14, was run by 183 users (up 30% from 

last year) from 10 countries. 

The major milestone in OOF development during 

FY11 was the February release of version 2.1.0, which 

allowed for the solution of time dependent problems 

and included more robust nonlinear solvers, as well as 

a large number of improved features and bug fixes. 

Four subsequent bug-fix releases brought the version 

 

14 http://nanoHUB.org/

number up to 2.1.5. A complete description of the new 

features of version 2.1.0 is available online15. 

The new, more flexible nonlinear solvers were 

used by a highly nonlinear elastic constitutive model, 

which demonstrated the facility and correctness of the 

OOF extension scheme; this work was presented at 

FEMTEC 2011, a finite-element modeling conference 

which represents a new audience for the OOF software. 

Other work during FY11 concentrated on three 

topics: surface properties (Andrew Reid), image segmentation (Günay Doğan), and three dimensions (Steve 

Langer and Valerie Coffman). 

Surface properties in OOF2 assign material characteristics to the boundary between two materials in a 

microstructure, in contrast to bulk properties, which 

determine the behavior of a single material away from 

the boundaries. It was discovered that the existing surface property infrastructure did not make effective use 

of the main solver routines, so a new surface property 

scheme was constructed which would be better integrated with the bulk solvers. In the process, a bug was 

identified in the automatically generated surface 

boundary conditions, which are used to tie together 

field values across an interface, and also used to implement periodic boundary conditions. This 

necessitated a review of some of the boundary condition code, and the construction of a new class of 

boundary conditions for the out-of-plane parts of the 

fields. Implementation of surface properties then proceeded, and has reached the point where surfacespecific constant-flux contributions can be correctly 

represented. 

Image segmentation is the problem of identifying 

distinct regions or objects in a given image. This is the 

first step for microstructure analysis with OOF. During 

FY11 a powerful class of segmentation models was 

implemented, applicable to a wealth of images in material science as well as other domains, particularly those 

of interest to the NIST Innovations in Measurement 

Science Project on Shape Metrology, which was initiated this year. The underlying principle of the approach 

is energy minimization. Shapes, such as curves or surfaces, are assigned energies which are minimized when 

the shapes are aligned with boundaries in the image. 

The algorithm works by iteratively deforming specified 

 

15 http://www.ctcms.nist.gov/oof/oof2/new_in_21.html
Summary of Activities for Fiscal Year 2011 71 

initial shapes until an energy minimum is obtained. 

The infrastructure to do this in two dimensions is now 

complete, including algorithms for shape optimization, 

topological changes (to adjust the number of curves 

when finding an unknown number objects), and handling image boundaries. A significant portion of the 

development effort went into making the method efficient for large images, using adaptivity to save CPU 

time while preserving accuracy, efficient linear algebra 

to take advantage of the special structure of the problem, Newton-type descent methods to reduce the 

number iterations needed, and a separate algorithm to 

get good starting points in certain cases. 

Progress on the three dimensional code, OOF3D, 

was slowed somewhat by the July departure of Valerie 

Coffman, who had been leading the effort. At that 

point, OOF3D could perform all of the steps required 

to perform a complete calculation in a minimal fashion. 

It lacked a working test suite, though, and was therefore not ready for release. Since then efforts have 

concentrated on the test suite, with several long diversions to fix bugs or add features necessary to make the 

program easy to use. An initial alpha release of 

OOF3D is expected in FY12. 

In addition to the above topics, a significant effort 

was spent on user support, such as regression testing of 

OOF2 releases on many operating systems, including 

OS X, NetBSD and a number of Linux distributions. 

This task has been simplified by the availability of mature virtualization tools. 

[1] A. Reid, Object-Oriented Finite Element Materials 

Modeling at NIST, 3rd International Conference on 

Computational Methods in Engineering and Science 

(FEMTEC 2011), Stateline, NV, May 9, 2011. 

Micromagnetic Modeling 

Michael Donahue 

Donald Porter 

Robert McMichael (NIST CNST) 

June Lau (NIST MML) 

http://math.nist.gov/oommf/

Advances in magnetic devices such as recording heads, 

field sensors, magnetic nonvolatile memory (MRAM), 

and magnetic logic devices are dependent on an understanding of magnetization processes in magnetic 

materials at the nanometer level. Micromagnetics, a 

mathematical model used to simulate magnetic behavior, is needed to interpret measurements at this scale. 

ACMD is working with industrial and academic partners, as well as with colleagues in the NIST CNST, 

MML, and PML, to improve the state-of-the-art in micromagnetic modeling. 

 Michael Donahue and Donald Porter in ACMD 

have developed a widely used public domain computer 

code for doing computational micromagnetics, the Object-Oriented Micromagnetic Modeling Framework 

(OOMMF). OOMMF serves as an open, welldocumented environment in which algorithms can be 

evaluated on benchmark problems. OOMMF has a 

modular structure that allows independent developers 

to contribute extensions that add to the basic functionality of OOMMF. OOMMF also provides a fully 

functional micromagnetic modeling system, handling 

both two and three-dimensional problems, with sophisticated extensible input and output mechanisms. 

In FY 2011 alone, the software was downloaded 

more than 5,000 times, and use of OOMMF was 

acknowledged in 129 peer-reviewed journal articles. 

OOMMF has become an invaluable tool in the magnetics research community. 

Key new developments in OOMMF over the last 

year include: 

- Implemented 1D periodic boundary conditions, 

including development of techniques to improve 

accuracy and accelerate convergence of the infinite 

sums needed to compute long-range magnetostatic 

fields. These methods work well when the computational cells are nearly cubes, but are not accurate 

for cells with large aspect ratios. 

- Implemented two preconditioners for the conjugate-gradient solver, improving computation speed 

of simulations with highly non-uniform edges by a 

factor of ten. 

- Continued development on measurement, analysis, 

and improvement of the performance of multithreaded computations on non-uniform memory 

access (NUMA) architectures. Major issues include effective propagation of task requests to and 

wake-up latency of worker threads. 

Ongoing work includes extension of periodic 

boundary condition support to two dimensions, refinement of asymptotic approximations to improve 

accuracy for cells with large aspect ratio, and implementation of enhanced task dispatching techniques in 

multi-threaded operations. 

OOMMF is part of a larger activity, the Micromagnetic Modeling Activity Group (muMAG), formed 

to address fundamental issues in micromagnetic modeling through two activities: the development of public 

domain reference software, and the definition and dissemination of standard problems for testing modeling 

software. ACMD staff members are involved in development of the standard problem suite as well. There are 

currently four standard problems in the suite, testing 

both static and dynamic magnetization properties. A 

new standard problem proposed jointly by several authors [1] aims at validation of simulations of spin 

momentum transfer in the “current parallel to plane” 
 72 NIST Applied and Computational Mathematics Division 

geometry. A solver that computes spin momentum 

transfer is based on one of two competing equations. A 

standard problem must be stated in terms that solvers 

based on either equation can be directed to solve. 

While translating the proposed problem into these 

terms, it became apparent that extending the problem 

into a sequence of problems would enhance its usefulness. Each problem in the sequence prescribes a 

different value for the degree of non-adiabaticity, ξ. 

Solving the problem for small values of ξ achieves the 

goal of the original proposed problem, while larger 

values of ξ illustrate where the two competing equations diverge in their predictions. Testing of the 

proposed problem also revealed the importance of an 

explicit description of the boundary conditions to impose where current enters and leaves the magnetic 

material. 

In addition to the continuing development of 

OOMMF, the project also does collaborative research 

using OOMMF. The project plays an instrumental role 

in the 2007 NIST Innovation in Measurement Science 

project (with CNST, MML and PML), “Magnetic 

nanostructures for post-CMOS electronics.” This work 

involves development of methods for modeling polycrystalline materials with magnetically thick grain 

boundaries. 

In collaboration with the University of Konstanz 

we continue to use OOMMF to study magnetic structures in nanowires. Recent work has examined a novel 

pseudo-periodic domain structure of counter-rotating 

axial domains which may explain certain experimental 

findings of long period domain structures. The ACMD 

micromagnetic project produced one journal paper [2] 

and one conference presentation [3] this past year. 

[1] M. Najafi, et al., Proposal for a Standard Problem for 

Micromagnetic Simulations Including Spin-transfer 

Torque, Journal of Applied Physics 105 (2009), pp. 

113914-113921. 

[2] G. S. Abo, Y. K. Hong, B. C. Choi, M. J. Donahue, et 

al., Micromagnetic Computer Simulated Scaling Effect 

of S-shaped Permalloy Nano-element on Operating 

Fields for AND or OR Logic, IEEE Transactions on 

Magnetics, to appear. 

[3] M. Donahue, Parallelizing a Micromagnetic Program for 

Multi-processor Non-uniform Memory Access Computers, Conference on Magnetism and Magnetic Materials, 

Atlanta, GA, Nov. 15, 2010. 

Parallel Adaptive Refinement and 

Multigrid Finite Element Methods 

William F. Mitchell 

Marjorie A. McClain 

James Benson 

Eite Tiesinga (NIST PML) 

Thomas Hanna (NIST PML) 

John Villarrubia (NIST PML) 

Pavel Solin (University of Nevada, Reno) 

http://math.nist.gov/phaml

Finite element methods using adaptive refinement and 

multigrid techniques have been shown to be very efficient for solving partial differential equations. Adaptive 

refinement reduces the number of grid points by automatically concentrating the grid in the areas where the 

action is, and multigrid methods solve the resulting 

linear systems in an optimal number of operations. 

Recent research has been with hp-adaptive methods 

where adaptivity is in both the grid size and the polynomial order of approximation, resulting in exponential 

rates of convergence. W. Mitchell has been developing 

a code, PHAML, to apply these methods on parallel 

computers. The expertise and software developed in 

this project are useful for many NIST laboratory programs, including those in material design, 

semiconductor device simulation, and the quantum 

physics of matter. 

This year the effort was primarily focused on a 

study of the performance of several proposed hpadaptive strategies; see page 27. But the development 

and application of PHAML continue to be of prime 

importance. For example, as multicore computers 

begin to dominate the market, additional models of 

parallelism need to be implemented in scientific software. During the past year we have added OpenMP 

directives to PHAML to implement a shared memory 

model. Not only is this appropriate for a multicore 

computer, but it can be combined with the previously 

implemented MPI message passing model to form a 

hybrid MPI/OpenMP model that uses shared memory 

parallelism on the multicore nodes of a cluster and 

message passing between the nodes. 

A number of collaborative efforts to apply 

PHAML took place during this year: 

- In collaboration with Prof. Pavel Solin of the University of Nevada at Reno, PHAML has been 

added to FEMhub16. FEMhub provides a unified 

Python interface on top of open source finite element packages. PHAML is the second FEM 

package in FEMhub, after Prof. Solin's own finite 

element software. 

 

16 http://FEMhub.org/
Summary of Activities for Fiscal Year 2011 73 

- In collaboration with Eite Tiesinga and Tom Hanna of the NIST Physical Measurement Laboratory 

(PML), PHAML is being used to calculate the 

bound states, scattering properties, and dynamics 

of two dipolar molecules held in a cylindrically 

symmetric trap. We have studied in detail the twobody energy spectrum, and shown for the first time 

that the trap may be used to actively control the 

strength of the interactions. 

- We began a new collaboration with John Villarrubia of NIST PML to apply PHAML to the 

modeling of scanning electron microscope images 

of samples that contain a mixture of conducting 

and insulating regions. Villarrubia has a code that 

models electron scattering in materials, secondary 

electron production, and detection. This code will 

be coupled with PHAML which will perform the 

finite element analysis to determine the electric 

fields that affect the image. 

- James Benson is using PHAML to solve a coupled 

system of advection diffusion equations to model 

the fluid and concentration fields in a two domain 

system. One domain corresponds to the exterior 

region surrounding a tissue and the other domain is 

the interior of the tissue. 

Future work will continue to enhance PHAML 

with additional capabilities, robustness and efficiency, 

implement and study some recently proposed hpadaptive strategies, and extend PHAML to solve 3D 

problems, which is needed for both the work with Villarrubia and a new application with Tiesinga involving 

the collision of one atom and a di-atomic molecule. 

[1] W.F. Mitchell and M.A. McClain, A Survey of hpAdaptive Strategies for Elliptic Partial Differential 

Equations, in Recent Advances in Computational and 

Applied Mathematics (T.E. Simos, ed.), Springer, 2011, 

pp. 227-258. 

[2] W.F. Mitchell and M.A. McClain, A Comparison of hpAdaptive Strategies for Elliptic Partial Differential 

Equations, submitted. 

[3] W.F. Mitchell and M.A. McClain, A Comparison of hpAdaptive Strategies for Elliptic Partial Differential 

Equations (long version), NISTIR 7824, 2011. 

[4] W.F. Mitchell, A Collection of 2D Elliptic Problems for 

Testing Adaptive Algorithms, NISTIR 7668, 2010. 

[5] T.M. Hanna, E. Tiesinga, W.F. Mitchell and P.S. Julienne, Resonant Control of Polar Molecules in an 

Optical Lattice, arXiv:1111.0227v1, 2011. 

[6] W.F. Mitchell and M.A. McClain, Performance of hpAdaptive Finite Element Methods, SIAM Conference on 

Computational Science and Engineering, Reno, NV, 

February 2011. 

[7] T.M. Hanna, E. Tiesinga, W.F. Mitchell and P.S. Julienne, Bound States of Interacting Polar Molecules in 

an Optical Lattice, 42nd Annual DAMOP Meeting, Atlanta, GA, June 2011. 

[8] W.F. Mitchell and M.A. McClain, Comparison of hpAdaptive Finite Element Strategies, Foundations of 

Computational Mathematics, Budapest, July 2011. 

Finite Differences Using Voronoi 

Cells 

Javier Bernal

Nicos Martys (NIST EL)

A finite difference scheme based on Voronoi cells is 

being developed for numerical modeling of the diffusion operator on arbitrary unstructured grids. For the 

purpose of computing Laplace interpolants associated 

with Voronoi neighbors, programs will be implemented 

for computing volumes of Voronoi cells, areas of Voronoi facets, and distances between neighbors in 3-d 

Voronoi diagrams, as well as areas of Voronoi cells, 

lengths of Voronoi faces, and distances between Voronoi neighbors in 2-d Voronoi diagrams. 
 74 NIST Applied and Computational Mathematics Division 

Digital Library of Mathematical Functions 

The special functions of applied mathematics are fundamental tools enabling modeling and analysis in all 

areas of science and engineering. To make effective use of such functions, practitioners must have ready access to a reliable source of information on their properties. The goal of this work is the development and 

dissemination of definitive reference data on the special functions of applied mathematics. The centerpiece of 

this effort is the DLMF, a freely available interactive and richly linked online resource.

Digital Library of Mathematical 

Functions 

Daniel Lozier 

Ronald Boisvert 

Marjorie McClain 

Bruce Miller 

Frank Olver 

Bonita Saunders 

Abdou Youssef 

Brian Antonishek (NIST ITL) 

Charles Clark (NIST PML) 

http://dlmf.nist.gov/

Nearly half a century ago, in 1964, NBS published the 

immensely influential Handbook of Mathematical 

Functions, edited by Milton Abramowitz and Irene 

Stegun. Known simply as A&S, it can be found on the 

reference shelf of physicists, other scientists, engineers, 

and applied mathematicians all over the world. This 

has made it the best-selling NIST/NBS publication of 

all time. The trend of citations to A&S until recently 

has actually been increasing. These attributes are due 

in large part to the care with which it was produced by 

a carefully assembled team of subject area specialists 

who produced a largely error-free compendium of the 

most important formulas for mathematical special 

functions according to their use in research and scientific applications. In short, A&S became the standard 

reference for the properties of the special functions. 

 It is a testament to the universality of mathematics 

that an old standard can have such vital force today. 

But mathematics and ways of applying mathematics 

have not stood still, and for many years there have been 

calls for a new standard. Creating this new standard 

was the purpose of the DLMF Project. Conceived, 

funded, and led by NIST, the project was initiated in 

1997, and after long years of effort it released the 

online Digital Library of Mathematical Functions and 

its print companion, published by Cambridge University Press, in May 2010. The DLMF Project adopted the 

A&S method of production, with over 50 carefully selected and highly qualified contributors from 10 

different countries, but strengthened and expanded it in 

several significant ways: (a) every formula has a link to 

a proof, (b) every chapter was reviewed by a referee 

unknown to the author, (c) twice the number of formulas and many more graphs are included, (d) preferred 

notations are clearly stated and related to alternative 

notations, and (e) brief accounts of illustrative scientific applications are included. The online website 

provides: (a) links to software rather than voluminous 

numerical tables, (b) links to reviews and full texts of 

references, (c) internal links to the DLMF definition of 

each symbol in every displayed equation, (d) a way to 

download formulas for use by document processors, (e) 

interactive visualization of functions of two variables, 

and (f) an innovative math search engine. 

NIST is committed to maintain, update, and expand the mathematical content. A continuing need is to 

collect suggestions and reports of errors from users, 

investigate them, and respond to them by making 

changes on the website, and eventually in a reprinting 

of the Cambridge edition. This process led to Release 

1.0.1 on June 27, 2011, that included several text clarifications, additions to the bibliography, and 8 

corrections to five equations (of the nearly 10,000 in 

the DLMF), two tables, and one figure. The second and 

third releases on July 1 and August 29 identified several minor improvements affecting display on the 

website, and added a few more text clarifications and 

bibliographic citations; no errors in equations, tables, 

or figures were needed. In the future it is anticipated 

that chapters will be added, or existing chapters expanded, in a substantial second edition. 

NIST is also committed to building upon the expertise it developed to improve the dissemination of 

mathematical material on the web in ways that enable 

its more effective use by researchers and practitioners. 

For example, the processor developed at NIST for generating high-quality web display of mathematics 

encoded in LaTeX is the vehicle for the eventual inclusion of mathematical meaning, a capability that will 

allow formulas to be cut-and-pasted into computer algebra systems for use in subsequent symbolic 

processing. As a second example, an early prototype of 

a web service to produce standard reference tables for 

user-specified arguments and parameters, and to userspecified accuracy, has been constructed. This kind of 

table is unprecedented because the accuracy is guaran-
Summary of Activities for Fiscal Year 2011 75 

teed, not just estimated. These activities are being carried out in collaboration with other research groups, for 

example at Jacobs University in Germany and the University of Antwerp. Research collaborations in 

graphical visualization of functions and further development of the search capability are also in progress. 

Mathematical Knowledge 

Management 

Bruce Miller 

Abdou Youssef 

Michael Kohlhase (Jacobs University, Germany) 

Deyan Ginev (Jacobs University, Germany) 

Heinrich Stamerjohanns (Jacobs University, Germany) 

Our activity in Mathematical Knowledge Management 

(MKM) began in earnest with the Digital Library of 

Mathematical Functions (DLMF) project. Tools developed there soon found application outside. And, as 

often happens in science, those outside experiences 

bring benefits back to original project. 

Here, we primarily refer to LaTeXML [1], a tool 

developed in ACMD to convert DLMF's source documents from LaTeX into flexible XML formats. 

Naturally, the Web was a target, but supporting 

MathML improved usability, re-usability and accessibility. Additionally, rich XML formats accommodate a 

variety of enrichments, helping the user find relations 

between the mathematical functions and concepts. 

Interest in LaTeXML sprang up; a project [2] was 

begun at Jacobs University to convert the material in 

Cornell’s preprint archive (arXiv)17 from TeX to XML. 

Not only would it be available on the web, but it would 

serve as a test corpus for other MKM research such as 

mathematical search and semantic inference. The halfmillion-article arXiv is a strenuous test: the science 

may be first-rate, but the markup quality is highly variable. The planetary [3] project was then initiated to 

create Semantic Mathematical Wikis that would allow 

convenient and familiar authoring using LaTeX, and 

yet provide all the benefits of semantic representation 

of mathematics in terms of reuse, search and discovery 

of mathematical relationships. 

These projects have helped focus and drive development of LaTeXML. The arXiv project improved the 

robustness and coverage of the software. The dynamic 

environment of Wikis spurred the creation of a ‘Daemon’ process [4] which converts document fragments 

on the fly. 

 The real challenge, however, is ongoing work involving the generation of Content MathML, or 

semantic representation, of the mathematics. Always a 

 

17 http://arXiv.org/

goal, and further prodded by the planetary project, inferring the semantics of ambiguous markup is not 

necessarily always possible, short of full human intelligence (or AI?). Nevertheless, much can be inferred or 

clarified by augmenting the documents or, at least, recording and representing the ambiguities for later 

analysis. How such inferences are best done, on the one 

hand, and how to represent ambiguities, on the other, 

are continuing work [5]. Much infrastructural work 

within LaTeXML has been carried out to support such 

conversions and the interconnected parallel representations needed to make use of them. 

All of these developments eventually lead back to 

DLMF. Truly reusable mathematics based on content 

MathML will allow importing to other software such as 

computer algebra or graphics systems; perhaps even 

automated validation. Capabilities such as the planetary 

system could be used for mathematics-aware social 

media related to DLMF. Further, these enhancements 

along with others such as Scalable Vector Graphics 

generation from embedded graphical material and work 

towards supporting the ePub format will further improve the accessibility and portability of the DLMF. 

[1] B. Miller and A. Youssef, Technical Aspects of the Digital Library of Mathematical Functions, Annals of 

Mathematics and Artificial Intelligence 38 (2003), pp. 

121-136. 

[2] H. Stammerjohanns, M. Kohlhase, D. Ginev, C. David, 

and B. Miller, Transforming Large Collections of Scientific Publications to XML, Mathematics in Computer 

Science 3 (3) (2010), pp. 299-307.

[3] M. Kohlhase, et al., The Planetary System: Web 3.0 & 

Active Documents for STEM, in Proceedings of the 

2011 International Conference on Computational Science (M. Sato, S. Matsuoka, P.M. Sloot, G.D. van 

Albada and J. Dongarra, eds.), Volume 4, pp. 598-607. 

[4] D. Ginev, H. Stammerjohanns, B. Miller, and M. Kohlhase, The LaTeXML Daemon: Editable Math on the 

Collaborative Web, Lecture Notes in Computer Science

6824 (2011), pp. 292-294. 

[5] D. Ginev, The Structure of Mathematical Expressions, 

Master’s Thesis, Jacobs University, 2011. 
 76 NIST Applied and Computational Mathematics Division 

DLMF Standard Reference Tables 

on Demand 

Bonita Saunders 

Bruce Miller 

Marjorie McClain 

Daniel Lozier 

Chris Schanzle 

Annie Cuyt (University of Antwerp) 

Stefan Becuwe (University of Antwerp) 

Franky Backeljauw (University of Antwerp) 

Published tables have long been used to supply numerical values of elementary and special functions for 

numerical exploration, software validation, program 

debugging, algorithm construction, and graphics production. For example, the original special function 

procedures in Mathematica were validated by comparison with the 1964 NBS Handbook of Mathematical 

Functions. More recently, a communication was received from Microsoft seeking assistance with the 

validation of functions in its own numerical library, 

which is under development. 

The goal of our project is to develop a website at 

NIST that provides 21st century tools to escape the 

severe limitations of many previously published tables: 

low precision, sparsity of arguments and parameters, 

lack of coverage of complex variables, and inability to 

accommodate alternate function definitions. Our site 

will allow users to specify (within reasonable limits) 

these attributes, and it will return values with an accuracy certification. 

The first phase of the project, computing tables of 

high precision function values at real inputs assumed to 

be exact, is well underway. We first searched for reliable reference software, that is, software that establishes 

an error bound, preferably a priori, along with each 

function value. Such a package has been developed by 

a group at the University of Antwerp under the leadership of Prof. Dr. Annie Cuyt [1]. Their software 

package, which uses continued fractions as the main 

tool, covers a substantial subset of the functions included in the DLMF. After discussions at a NIST 

meeting in October 2010, we decided to collaborate 

with Dr. Cuyt’s group and developed an action plan. 

The NIST team worked on the front end user interface 

and the web software for the system, while Cuyt’s 

group refined the software for the computational engine. In December 2011 the two groups met again at 

NIST to integrate the various parts for a preliminary 

system with a small number of functions. During the 

two week meeting a selected group of testers at NIST 

and the University of Antwerp were given access to the 

system to provide feedback. Over the next few months 

more functions will be included, and additional modifications and testing will be conducted before the site is 

expanded into a prototype that will be released for wider testing. 

[1] A. Cuyt, F. Backeljauw, S. Becuwe, and J. Van Deun, 

Validated Special Functions Software, Lecture Notes in 

Computer Science 6327 (2010), pp. 32-34. 

ITL Program: Virtual Measurement Systems 

Figure 42. Prototype of DLMF Standards Reference Tables.
Summary of Activities for Fiscal Year 2011 77 

Visualization of Complex Functions 

Data 

Bonita Saunders 

Brian Antonishek (NIST ITL) 

Qiming Wang 

Bruce Miller 

Sandy Ressler 

Daniel Lozier 

Frank Olver 

During the development of the NIST Digital Library of 

Mathematical Functions (DLMF), a considerable effort 

was invested in creating accurate user-friendly visualizations to help users understand the behavior of 

complex functions. We have continued to improve these visualizations by developing better computational 

grids and redesigning the computation and movement 

of cutting planes used in interactive 3D visualizations. 

However, we would also like to increase accessibility 

to the interactive 3D visualizations. The current visualizations are rendered using two common technologies 

for 3D graphics on the web: Virtual Reality Modeling 

Language (VRML) and X3D. Users may view the visualizations by downloading a free plugin. While 

several viewers are available for Windows and Mac 

platforms, we have not found an acceptable Linux 

viewer that easily handles all the custom features implemented in our visualizations. Also, we must 

continually test the visualizations to catch anomalies 

that arise when the plugin, browser, or operating system is updated. We are addressing the accessibility 

problem in two ways: constructing a DLMF PDF file 

with embedded graphics, and adding the appropriate 

software code and modifications to our graphics files to 

allow users to see our visualizations on a web page 

without the use of a plugin. 

Creation and testing of the enhanced DLMF PDF 

file with embedded graphics has been completed. With 

a common PDF reader users can rotate 3D function 

surfaces, use the zoom feature, and explore other builtin options. We were concerned that the embedded 

graphics would greatly increase the size of the PDF 

file, but were relieved to find that it increased by only 

10 MB from about 25 MB to 35 MB. The other concern was that the embedding process would have to be 

redone every time the DLMF database and PDF file 

were regenerated. Fortunately, we found a package that 

would embed the graphics files directly into the DLMF 

LaTeX source files before PDF conversion. 

We are also attacking the accessibility problem 

from another direction by determining the modifications needed to view our files in a WebGL environenvironment. HTML5 contains WebGL attributes that 

allow users to view interactive graphics inside a web 

page without the need of a special plugin. Our X3D 

graphics files can be integrated with HTML5 via the 

X3DOM open source framework. We have successfully displayed simplified versions of some of our files in 

HTML5 browsers. An example is shown in Figure 43. 

The latest versions of several browsers now support 

WebGL, but for a while we will still need to provide 

files that are viewable with VRML/X3D plugins. 

[1] B. Saunders and Q. Wang, Tensor Product B-Spline 

Mesh Generation for Accurate Surface Visualizations in 

the NIST Digital Library of Mathematical Functions, 

Mathematical Methods for Curves and Surfaces, in Revised Selected Papers of the Seventh International 

Conference (MMCS 2008), Tonsberg, Norway, June 26-

July 1, 2008, Lecture Notes in Computer Science 5862 

(2010), pp. 385-393. 

[2] B. Saunders and Q. Wang, Tensor Product Grid Generation for Complex Surface Visualizations in a Digital 

Library of Mathematical Functions, in Proceedings of 

the 11th International Society for Grid Generation 

(ISGG) Conference, Montreal, Canada, May 25-28, 

2009, p. SV.3. 

[3] Q. Wang , B. Saunders, and S. Ressler, Dissemination of 

3D Visualizations of Complex Function Data for the 

NIST Digital Library of Mathematical Functions, CODATA Data Science Journal 6 (2007) (Supplement on 

the Proceedings of the 20th International CODATA Conference, Beijing, China, October 2006), pp. S146- S154. 

[4] B. Saunders, and Q. Wang, From B-Spline Mesh Generation to Effective Visualizations for the NIST Digital 

Library of Mathematical Functions, in Curve and Surface Design: Avignon 2006, Sixth International 

Conference on Curves and Surfaces, Avignon, France, 

Nashboro Press, 2007, pp. 235-243. 

Figure 43. Modulus of elliptic umbilic canonical integral function

|(E) (x,y,0)| displayed in HTML5 using X3DOM.
 78 NIST Applied and Computational Mathematics Division 

Quantum Information 

An emerging discipline at the intersection of physics and computer science, quantum information science 

(QIS) is likely to revolutionize science and technology in the same way that lasers, electronics, and computers did in the 20th century. By encoding information into quantum states of matter, one can, in theory, exploit 

the seemingly strange and counter-intuitive behavior of quantum systems to enable phenomenal increases in 

information storage and processing capability, as well as communication channels with extremely high levels 

of security. Although many of the necessary physical manipulations of quantum states have been demonstrated experimentally, scaling these up to enable fully capable quantum computers remains a grand challenge. 

We are engaged in (a) theoretical studies to understand the true power of quantum computing, (b) collaborative efforts with the multi-laboratory experimental quantum science program at NIST to characterize and 

benchmark specific physical implementations of quantum information processing, and (c) the development 

and assessment of technologies for quantum communication. 

Single Photon Upconversion and 

Quantum Information Science 

Xiao Tang 

Lijun Ma 

Oliver Slattery 

Barry Hershman 

Alan Mink 

Martin J. Stevens (NIST PML) 

Joshua C. Bienfang (NIST PML) 

Matthew T. Rakher (NIST CNST) 

Marcelo Davanço (NIST CNST) 

Kartik Srinivasan (NIST CNST) 

See feature article, page 40. 

ITL Program: Quantum Information

Quantum Computing Benchmarks 

Emanuel Knill 

Adam Meier 

Dietrich Leibfried (NIST PML) 

David Wineland (NIST PML) 

Quantum computing is still in its infancy. There are 

many experimental efforts involving a diverse collection of physical systems and engineering platforms for 

implementing the basic tasks, but it is still not possible 

to routinely implement even two-quantum-bit (qubit) 

quantum computations. To compare the different platforms in a standardized way, we are involved in 

developing and implementing benchmark procedures to 

evaluate the quality of basic quantum computing operations. In previous years, we developed a standard 

method for determining an error per gate (EPG) for 

one-qubit computations that is being implemented on 

an increasing number of platforms, ranging from nuclear magnetic resonance (NMR) spectrometers to ion 

traps. This year we participated in a new implementation of this benchmark in an ion trap where the qubits 

are manipulated with microwaves instead of laser light. 

This implementation successfully demonstrated EPGs 

below the critical value of 0.0001, which is believed to 

be necessary for practical scalable quantum computing. 

An important question is how to standardize such 

benchmarks for more than one qubit. We developed a 

technique that can do this by requiring the experimenter to implement random sequences of so-called 

Clifford unitary operators. By specifying the family of 

operators rather than the specific elementary steps required to implement them, the benchmark can be 

realized on any platform, independent of the details of 

the underlying physics. The family of operators is welldefined for any number n of qubits, and implementing 

a random such operator typically requires of the order 

of n2

 elementary steps. As a result, the ability to implement them is already a demonstration of the power 

of a platform. 

Our benchmarks are not intended to diagnose the 

causes for imperfections in gates. Their main purpose 

is to compare different computing platforms at different stages of their development. Nevertheless, it would 

be helpful if some diagnostics were available. For this 

purpose, we modified the Clifford-unitary-based 

benchmark so that individual operations to be characterized can be inserted between steps. This makes it 

possible to determine an EPG for such operations. 

The two benchmarking ideas of the above paragraphs were implemented in an ion trap developed by 

the NIST Ion Storage group. This ion trap is a testbed 

for many of the technologies needed to scale up iontrap quantum computing. In particular, it includes multiple trapping zones where the ions can be manipulated, 

and it realizes a sympathetic cooling strategy whereby 

the qubit-ions are cooled by an ion of a different atomic species. The benchmark was realized with two qubitions and implemented up to six random Clifford unitaries in sequence. A key two-qubit operation, the phase 

gate, was characterized and shown to have an EPG of 
Summary of Activities for Fiscal Year 2011 79 

about 0.07. While this is far from sufficient for scalable 

quantum computing, and other experiments have indicated lower EPGs in restricted settings, the experiment 

shows that our proposed two-qubit benchmark is feasible and able to characterize individual gates. 

The relationship between the benchmark EPG and 

the actual error behavior of underlying operations is 

understood only in highly idealized situations. However, these benchmarks provide useful, standardized 

methods for comparing quantum computing platforms. 

We are developing guidelines for ensuring that the 

EPG computed from the benchmarks is meaningful. 

The guidelines include suggestions for consistency 

checks that should be performed. Further theoretical 

work is required to investigate the relationship between 

benchmark EPGs and the physical error behavior in 

practical settings. 

[1] K.R. Brown, A.C. Wilson, Y. Colombe, C. Ospelkaus, 

A.M. Meier, E. Knill, D. Leibfried, and D.J. Wineland, 

Single-Qubit-Gate Error Below 10-4 in a Trapped Ion, 

Physical Review A 84 (2001), article 030303(R)/1-4. 

[2] J.P. Gaebler et al., Randomized Benchmarking of TwoQubit Gates, in progress. 

ITL Program: Quantum Information

Quantum State Estimation Theory 

and Applications 

Scott Glancy 

Emanuel Knill 

Burm Baek (NIST PML) 

Bryce Calkins (NIST PML) 

Gene Hilton (NIST PML) 

Kent Irwin (NIST PML) 

Thomas Gerrits (NIST PML) 

Konrad Lehnert (NIST PML) 

Adriana Lita (NIST PML) 

Richard Mirin (NIST PML) 

Sae Woo Nam (NIST PML) 

Martin Stevens (NIST PML) 

Leila Vale (NIST PML) 

Ryan Bennink (Oak Ridge National Laboratory) 

Sander Dorenbos (Delft University of Technology, NL) 

Warren Grice (Oak Ridge National Laboratory) 

Robert Hadfield (Heriot-Watt University, UK) 

Will Kindel (University of Colorado) 

Tuen Klapwijk (Delft University of Technology, NL) 

Hsiang S. Ku (University of Colorado) 

Tony Zijlstra (Delft University of Technology, NL) 

Val Zwiller (Delft University of Technology, NL) 

Many emerging technologies will exploit quantum mechanical effects to enhance metrology, computation, 

and communication. Developing these technologies 

requires improved methods to measure the state of 

quantum systems. Quantum state estimation is a statistical problem of estimating an underlying quantum 

state using a collection of measurements made on independently prepared copies of the state. Accurate 

quantum state estimation allows experimentalists to 

answer the questions “What quantum state does my 

device prepare?” and “How confident am I that it has 

prepared that state?” In the last year we have focused 

on collaborations with two experimental groups using 

quantum state estimation. 

The first of these is an experiment to prepare 

squeezed light for quantum information processing 

applications. The creation of high quality squeezed 

light is helpful for quantum enhanced interferometry, 

optical quantum computation, and other technologies. 

However, these technologies are limited by the quality 

of squeezed light, which is often contaminated with 

photons in pulses that overlap the primary squeezed 

pulse and whose mode structure is not suitable for 

some intended applications. Experimentalists in our 

team engineered a nonlinear crystal and laser pumping 

strategy to produce highly pure squeezed light, and 

ACMD members helped to design a measurement and 

analysis strategy to demonstrate the experiment's success in avoiding contaminating photons and matching 

the desired pulse shapes. We showed world record 

overlap of two entangled, squeezed pulses and published the results in Optics Express. 

The second experiment is the DARPA-funded collaboration with JILA, “Analog Quantum Integrated 

Circuits.” The goal of this project is to create entangled 

states in superconducting microwave circuits and to use 

that entanglement for quantum teleportation. In 2011 

we prepared an entangled state of quantum microwaves 

and verified the entanglement with preliminary measurements, which will be presented at the American 

Physical Society's March Meeting in 2012. We are 

developing methods to calibrate the measurements and 

fully quantify the amount of entanglement. 

[1] T. Gerrits, M.J. Stevens, B. Baek, B. Calkins, A. Lita, S. 

Glancy, E. Knill, S.-W. Nam, R.P. Mirin, R.H. Hadfield, 

R.S. Bennink, W.P. Grice, S. Dorenbos, T. Zijlstra, T. 

Klapwijk, and V. Zwiller, Generation of Degenerate, 

Factorizable, Pulsed Squeezed Light at Telecom Wavelengths, Optics Express 19 (2011) article 24434. 

[2] W. Kindel, H.S. Ku, S. Glancy, E. Knill, K.D. Irwin, G. 

C. Hilton, L.R. Vale, and K.W. Lehnert, Generating Distributable and Unconditional Entanglement on-chip at 

Microwave Frequencies, accepted, APS March Meeting, 

Boston, MA, Feb. 27, 2012. 

[3] H.S. Ku, W. Kindel, S. Glancy, E. Knill, K. D. Irwin, G. 

C. Hilton, L.R. Vale, and K.W. Lehnert, Quantifying 

Distributable and Unconditional Entanglement at Microwave Frequencies, accepted, APS March Meeting, 

Boston, MA, Feb. 27, 2012.

ITL Program: Quantum Information
 80 NIST Applied and Computational Mathematics Division 

Quantum State Tomography using 

Compressed Sensing 

Yi-Kai Liu 

Steven T. Flammia (Caltech) 

Quantum state tomography is a family of techniques 

for estimating the state of a quantum system. Tomography provides a full characterization of the state, 

including all effects due to noise and decoherence. This 

makes it a useful tool in experiments involving quantum-enhanced metrology and quantum computation. 

However, tomography of large quantum systems is 

very resource-intensive: for a system of n qubits, 

standard methods of tomography require measuring 4n

different observables. 

Recently it was shown that tomography can be 

done using far fewer measurements, using compressed 

sensing techniques, provided that the state is low-rank 

or pure — a condition that is satisfied in most experiments [1]. In particular, if the state has rank r, then it is 

sufficient to measure only O(2n r poly(n)) Pauli observables, in order to completely characterize the state. 

Furthermore, given the measurement data, one can 

compute the density matrix easily, by solving a traceminimization convex program. This approach is known 

as compressed tomography. 

In the last year, the first tight error bounds were 

determined for compressed tomography [2]. These 

quantify how the error in the estimated density matrix 

depends on errors in the measurement data. They also 

give the first useful bounds on the sample complexity 

of compressed tomography. (Sample complexity describes how many copies of the unknown state are 

required.) These results are obtained from a new analysis of compressed tomography using the restricted 

isometry property (RIP) [2,3]. 

Roughly speaking, a mapping satisfies RIP if it 

approximately preserves the geometry (as measured by 

the 2-norm) of the set of low-rank matrices. In [2], it is 

shown that the random Pauli sampling operator satisfies RIP with high probability. This is quite surprising, 

because the sampling operator embeds a nonlinear 

manifold (the set of all low-rank matrices) into a linear 

space, with only a slight increase in the dimension. The 

proof of this claim is highly nontrivial: it uses Dudley’s 

inequality for bounding the supremum of a Gaussian 

process, and bounds on covering numbers using entropy duality. Then, once RIP is established, the results of 

[3] imply error bounds for compressed tomography. 

These error bounds complete our understanding of 

the practical resource requirements for compressed 

tomography. It was known before that compressed tomography uses fewer measurement settings and less 

classical postprocessing than standard tomography. 

The new error bounds show that compressed tomography has roughly the same sample complexity as 

standard tomography (up to log factors). Thus, there is 

no “hidden cost” in the sample complexity. In fact, this 

sample complexity is nearly optimal, in the sense that 

no scheme for pure-state tomography using Pauli 

measurements can do better (up to log factors) [4]. 

The next major step in this project will be an experimental demonstration of compressed tomography, 

likely using ion traps. To this end, it will be useful to 

develop faster algorithms for solving the traceminimization convex program. The algorithm in [1], 

singular value thresholding (SVT), can reconstruct the 

density matrix for about 8 qubits on a laptop computer. 

It may be possible to handle more qubits, using parallel 

versions of the algorithm, or alternative optimization 

techniques such as gradient descent on the Grassmannian manifold. Also, it will be interesting to construct 

estimators that combine the compressed sensing approach with traditional maximum-likelihood estimation 

(MLE), e.g., trace-norm-regularized MLE. Finally, one 

might hope to adapt compressed sensing techniques to 

continuous-variable systems, e.g., optical homodyne 

tomography. 

[1] D. Gross, Y.-K. Liu, S.T. Flammia, S. Becker, and J. 

Eisert, Quantum State Tomography via Compressed 

Sensing, Physical Review Letters 105 (2010), article 

150401. 

[2] Y.-K. Liu, Universal Low-rank Matrix Recovery from 

Pauli Measurements, in Advances in Neural Information 

Processing Systems (NIPS 2011), to appear. 

[3] E.J. Candès and Y. Plan, Tight Oracle Inequalities for 

Low-Rank Matrix Recovery from a Minimal Number of 

Noisy Random Measurements, IEEE Transactions on 

Information Theory 57 (4) (2011), pp. 2342-2359. 

[4] S.T. Flammia and Y.-K. Liu, Direct Fidelity Estimation 

from Few Pauli Measurements, Physical Review Letters

106 (2011), article 230501. 

ITL Program: Quantum Information

Quantum Computing Theory 

Scott Glancy 

Emanuel Knill 

Adam Meier 

Mike Mullan 

Yanbao Zhang 

Bryan Eastin (Northrop Grumman) 

Emilio Cobanera (Indiana University) 

Gerardo Ortiz (Indiana University) 

Our theoretical work on quantum computing and information progressed in four main areas this year. We 

developed and implemented a new and statistically 

rigorous method for analyzing demonstrations of nonclassicality in experiments, we formalized a method of 

optimizing phase interrogations for atomic clocks and 
Summary of Activities for Fiscal Year 2011 81 

initiated a program to test the method on simulations, 

we determined and analyzed a new method for “magic 

state” distillation, and we contributed to the theory of 

duality for quantum lattice models relevant to condensed matter studies. 

Our work on quantum lattice dualities is still preliminary. Our main contribution so far is to help 

establish new dualities involving so-called Hopfalgebraic one-dimensional lattice models. A hope is 

that such models may illuminate condensed matter 

systems of interest, though a more likely outcome is 

that they provide small examples for testing future analog quantum simulators such as those based on atoms 

in optical lattices. 

Magic-state distillation is a strategy envisioned for 

use in future fault-tolerant quantum computers, where 

it is required for universal computing. The distillation 

process improves initially noisy special states to the 

point where they are almost noise-free. The standard 

magic state distillation routines are based on a seven 

and a five quantum bit (qubit) error-correcting code. 

We investigated the use of a four qubit error-detecting 

code and found that it leads to a distillation routine 

requiring fewer resources per iteration. However, the 

distilled states improve less in comparison. We determined the exact behavior of the routine in combination 

with other routines and found that for a given reduction 

in noise, its use can reduce resources required by up to 

a factor of about 10. This should help reduce the large 

overheads for noise reduction in proposed methods for 

fault-tolerant quantum computing. 

Quantum methods for phase measurements used in 

modern atomic frequency standards and clocks promise 

to improve their precision over the shot-noise limit. 

The most advanced clocks being experimentally tested 

at NIST have the potential for using such methods, but 

the methods need to be modified from the theoretical 

ones to work in the presence of classical phase noise in 

the reference oscillators (“flywheels”) used. We have 

adapted semidefinite programming techniques from 

quantum query complexity to this problem and are currently testing them on simulated clocks. So far we have 

established that gains over conventional and theoretical 

quantum methods are possible in one clock interrogation step. In order to demonstrate this, we showed that 

the continuous phase estimation problem can be efficiently discretized for the purpose of semidefinite 

programming. Work in progress involves adapting our 

techniques to the situation where sequential interrogations are used to monitor frequency and phase. The 

main task is to implement a flexible simulator where 

we can choose the relevant noise model and keep track 

of the accumulated phase from previous interrogations. 

The best-known proof that quantum non-locality is 

not consistent with classical, local-realistic expectations is based on the quantum violation of Bellinequalities for two-party measurement outcomes that 

are satisfied by local realism. There still has not been a 

completely loop-hole free demonstration of such violation. The main obstacle is the difficulty of setting up an 

experiment with sufficiently low photon loss and large 

separation between the two parties making the measurements. Loop-hole-free demonstrations are also 

needed to enable many quantum information protocols. 

In the past, the (conditional) success of Bell-inequality 

experiments was quantified by the number of standarddeviations of violation of the inequality. We formally 

verified that this measure of success is not statistically 

justifiable, can lead to excessive confidence in violation, and cannot be compared between independent 

experiments. We remedied this situation by showing 

how a statistically rigorous p-value for violation of 

local realism can be computed for any experiment, independent of any particular Bell-inequality or the 

experimental setup. Our method is efficient and can be 

used “on-the-fly” to optimize experiments to enable 

more efficient protocols. We developed and released 

software that implements our method. 

[1] A. Meier, B. Eastin, and E. Knill, Magic-state Distillation with the Four-qubit Code, in progress. 

[2] Y. Zhang, S. Glancy, and E. Knill, Asymptotically Optimal Data Analysis for Rejecting Local Realism, 

arXiv:1108.2468, accepted, Physical Review A. 

[3] M. Mullan and E. Knill, Improving Quantum Clocks via 

Semidefinite Programming, arXiv:1107.5347, submitted.

ITL Program: Quantum Information

Quantum Algorithms for Quantum 

Field Theories 

Stephen Jordan 

Keith S. M. Lee (University of Pittsburgh) 

John Preskill (Caltech) 

Quantum field theory has wide-ranging applications in 

both high-energy and condensed-matter physics. In 

particular, it reconciles quantum mechanics with special relativity and provides the most fundamental 

theory of physics to be tested by experiment: the socalled Standard Model of particle physics. 

The question of whether quantum field theories 

can be efficiently simulated by quantum computers was 

first posed by Feynman three decades ago when he 

introduced the notion of quantum computers. Since 

then, efficient quantum algorithms have been developed to simulate the dynamics of quantum lattice 

models and quantum systems with a fixed number of 

particles, but the question about quantum field theories 

has remained open. 
 82 NIST Applied and Computational Mathematics Division 

We have developed a fast quantum algorithm for 

simulating relativistic particle scattering in a wellknown quantum field theory called phi-fourth theory. 

While simpler than the standard model, which encompasses all physical processes except those involving 

gravity, phi-fourth theory illustrates the essential challenges of simulating quantum field theories. 

The two most essential challenges in simulating 

quantum field theories on a quantum computer are discretization and state preparation. The discretization 

problem arises because, in principle, a quantum field 

has infinitely many degrees of freedom, even within 

finite volume. Thus, an exact description of the quantum state of the field requires infinitely many qubits. 

The obvious approach to this challenge is to discretize 

space onto a lattice. We show that this approach works, 

although it is nontrivial due to a uniquely quantum 

field-theoretic effect called renormalization. The state 

preparation problem is to design efficient quantum 

circuits that construct qubit representations of physically realistic initial states for the simulation. We achieve 

this by developing a new generalization of a widelyused quantum algorithmic technique called adiabatic 

state preparation. 

Upon successful construction of a large-scale 

quantum computer, a fast quantum algorithm for simulating quantum field theories will be useful in 

simulating processes from nuclear, particle, astronomical, and condensed-matter physics. Furthermore, the 

question of whether quantum field theories can be efficiently simulated by a quantum computer bears on the 

fundamental computational power of the universe. If 

quantum computers cannot efficiently simulate the 

Standard Model, this raises the possibility of quantum 

field computers exponentially more powerful than “ordinary” quantum computers. Conversely, if the 

methods introduced in this work can be extended to 

efficiently simulate the full Standard Model, this would 

definitively eliminate the possibility of such exponential speedups. 

[1] S.P. Jordan, K.S.M. Lee and J. Preskill, Quantum Algorithms for Quantum Field Theories, arXiv:1111.3633, 

submitted. 

ITL Program: Quantum Information

Post-Quantum Cryptography 

Stephen Jordan 

Yi-Kai Liu 

Ray Perlner (NIST ITL) 

Daniel Smith (NIST ITL) 

In 1994, Peter Shor discovered a polynomial-time 

quantum algorithm for factoring integers and computing discrete logarithms. This has far-reaching 

consequences for cryptography: if large-scale quantum 

computers are built, they would break essentially all of 

the public-key cryptosystems currently used for internet commerce, including RSA and elliptic curve 

cryptosystems. For this reason, we are beginning to 

study alternative cryptosystems that would be secure 

against quantum attacks. 

There are three main classes of cryptosystems that 

have been proposed to replace RSA: lattice-based (such 

as NTRU), code-based (such as McEliece), and multivariate (such as HFE and its variants). However, there 

are significant open questions regarding these proposals. For instance, many practical lattice-based 

cryptosystems use special classes of lattices, such as 

cyclic or ideal lattices, whose security is not as wellunderstood (compared to the case of general lattices). 

Indeed, ideal lattices have a surprisingly powerful algebraic structure, which is a topic of current research, 

and which enables tasks such as fully homomorphic 

encryption. On the other hand, code-based cryptosystems tend to have large key sizes, which would have a 

significant impact on the broader public-key infrastructure. To deploy these cryptosystems on a large scale, 

one will need better strategies for mitigating this impact. Finally, there have been successful attacks against 

some multivariate cryptosystems, and it is an interesting open problem to understand what algebraic features 

are sufficient to ensure the security of such schemes. 

There are also major open questions relating to 

quantum computation. First, what kinds of problems 

can be solved efficiently on a quantum computer? It is 

known that there are various ways in which quantum 

computers can achieve speed-ups over classical computers: for instance, using the quantum Fourier 

transform to solve certain algebraic problems involving 

hidden subgroups and hidden shifts; or using adiabatic 

evolution and quantum “tunneling” to solve certain 

combinatorial optimization problems. In particular, 

Shor’s algorithm is an example of the first strategy. In 

fact there are many other quantum algorithms that 

solve algebraic problems, and it is important to understand whether these algorithms are cryptographically 

relevant. 

In addition, we are monitoring ongoing developments in experimental quantum computation, in order 

to predict when (or whether) quantum computers will 

pose a significant threat to RSA and other cryptosystems currently in use. There are several different 

approaches to building large-scale quantum computers, 

including ion traps, adiabatic quantum computation, 

superconducting circuits, and topological anyons. The 

rate at which these technologies mature and scale up 

will determine when it becomes necessary to deploy 

new “quantum-resistant” cryptosystems. 

Finally, there is an interesting possibility that ideas 

from quantum information may lead to novel cryptographic protocols. Quantum key distribution is one 
Summary of Activities for Fiscal Year 2011 83 

well-known example, and we are considering others, 

including schemes for encrypted quantum computation 

based on braid groups, and implementations of secure 

hardware using non-orthogonal quantum states.

ITL Program: Quantum Information
 84 NIST Applied and Computational Mathematics Division 

Foundations of Measurement Science for Information Systems 

Modern information systems are astounding in their complexity. Software applications are built from thousands of interacting components. Computer networks interconnect millions of independently operating nodes. 

Large-scale networked applications provide the basis for services of national scope, such as financial transactions and electrical power distribution. In spite of our increasing reliance on such systems, our ability to 

build far outpaces our ability to secure. Protocols controlling the behavior of individual nodes lead to unexpected macroscopic behavior. Local power anomalies propagate in unexpected ways leading to large-scale 

outages. Computer system vulnerabilities are exploited in viral attacks resulting in widespread loss of data 

and system availability. The long term stability of our critical infrastructure is simply unknown. Measurement science has long provided a basis for the understanding and control of physical systems. Similar types 

of deep understanding and insight are lacking for complex information systems. We seek to develop the 

mathematical foundations needed for the emergence of a true measurement science for complex networked 

information systems. 

Community and Cluster Detection: 

Alternative Measures for Network 

Structure 

Roldan Pozo 

See feature article, page 42. 

ITL Program: Complex Systems

Algorithms to Approximate 

Multivariate Network Reliability 

Isabel Beichl 

Elizabeth Moseman 

Francis Sullivan (IDA Center for Computing Sciences) 

In estimating the reliability of a real-world network, 

one difficult but common problem is that of dealing 

with network connections of varying robustness. Some 

links might be easily broken while others are much less 

likely to fail. The situation to avoid in designing and 

maintaining a network is a set of weak links whose 

failure causes the whole network to collapse. A first 

step in attacking this problem is to devise algorithms to 

estimate the reliability of a multi-variate network—one 

in which every edge can have a different probability of 

failure. 

We think of the network as a graph G = (V,E) with 

V, the nodes, and E, the edges, connecting some of the 

nodes. We are also given a vector p = (pe)eE indexed 

by the edges, e, where pe is the probability that edge, e, 

is connected. There is a naive way to compute the 

probability of connection of such a multivariate network, namely, for each sample allow an existing edge 

to be connected with probability pe, for all e, and then 

determine if the resulting graph is connected. The percentage of times the resulting graph is connected will 

give an estimate of the reliability. However the variance of this simple “vanilla” method of Bernoulli trials 

is large, especially if the pe are small. 

We give two new probabilistic methods based on 

sequential importance sampling to approximate the 

reliability of the network. The strength of these algorithms is that they only look at local changes in the 

graph to make their estimates and have significantly 

lower variance than Bernoulli trials. 

The first of our new methods uses the formulation 

of reliability as a variation on computing the Tutte polynomial. In computing the Tutte polynomial for a 

graph, one builds a tree where at each node of the tree, 

one edge of the graph is examined. Since our edges 

have associated probabilities, pe, this gives us a way to 

select a path from the root of the tree of the Tutte polynomial to one of its leaves. 

 The probability at each tree node to remove the 

edge e in the resulting subgraph is 1-pe unless removing it would disconnect the graph. In that case, leave it 

in with probability one. The resulting subgraph is guaranteed to be connected. We are using importance 

sampling so that we choose with some probability q

and then divide by that probability, (pe if the edge is 

left in and 1-pe if it is removed). We have proved that 

in this algorithm all probabilities cancel except for the 

edges that would have caused a disconnection. The 

product of probabilities remaining gives an unbiased 

estimate of the reliability. A remarkable feature of this 

method is that, although the result itself is independent 

of the order in which the edges are chosen, the variance 

does, in fact, depend on order of selection. The optimal 

order is increasing probability pe. 

 The second new method is somewhat similar, except that the decision to remove an edge is made 

probabilistically over the set of all currently removable 

edges. This results in a different importance function 
Summary of Activities for Fiscal Year 2011 85 

with different cancellations and different variance behavior. If the pe are close to one, the second method has 

larger variance than the first. For small pe, the situation 

is reversed. In this case, the first method tends to behave like the “vanilla” method while the second 

method does better.

ITL Program: Complex Systems

New Importance Functions and 

Efficient Algorithms for Network 

Reliability 

 Isabel Beichl 

David G. Harris (National Security Agency) 

Francis Sullivan (IDA Center for Computing Sciences) 

We can think of a network as a graph, that is, a set of 

vertices V, and a set of edges, E, that connect two of 

the vertices. A graph is connected if there is a sequence of edges between any two vertices in V. The 

reliability polynomial of a graph gives the probability 

that a graph is connected as a function of the probability that each edge is connected. The coefficients of the 

reliability polynomial, ck, are the number of connected 

subgraphs of size k. The coefficients give more information about the network than the reliability alone. 

Computing the reliability polynomial is #P complete 

and so it is important to find probabilistic methods to 

approximate the coefficients. Sequential importance 

sampling (SIS) is a Monte Carlo method based on a 

statistical technique, importance sampling, which can 

often be used to reduce variance. 

Algorithms based on sequential importance sampling (SIS) were proposed to estimate a graph's 

reliability polynomial. We develop a new SIS algorithm that uses a new importance function based on the 

number of spanning trees to sample among the connected spanning subgraphs. The new method chooses a 

spanning tree at random and adds edges back until the 

original graph is recovered. The determinant of a certain matrix (the Laplacian) is known to give the 

number of spanning trees of a graph. This determinant 

is calculated at each stage of the importance sampling 

in order to give an importance function and in order to 

estimate the reliability coefficients. The complexity is 

controlled because each subgraph is built on previous 

subgraphs by adding only one edge, resulting in only 

rank one updates to the Laplacian matrix. This algorithm improves on existing algorithms in that it has 

lower complexity ~O(E2

) as opposed to O(E V3), and 

the new importance function does indeed reduce variance. Lower variance implies that each sample drawn 

is more efficient and that far fewer random samples 

need to be drawn, thus improving the state of the art 

from theoretical algorithms to practical computation. 

[1] D. Harris, F. Sullivan, and I. Beichl, Linear Algebra and 

Sequential Importance Sampling for Network Reliability, in Proceedings of the Winter Simulation Conference, 

Phoenix AZ, December 11-14, 2011. 

ITL Program: Complex Systems 

Affiliation Networks 

Brian D. Cloteaux 

James Shook 

Many networks can be naturally represented as relationships between entities and the groups (or 

affiliations) to which the entities belong. A network 

that records these relationships between the entities and 

the affiliations to which they belong is called an affiliation network. An example of a network and its 

associated affiliation network is shown in Figure 44. 

To understand what an affiliation network is, we 

can consider collaboration networks. A collaboration 

networks records authors who have worked together on 

papers. Thus it is typically a simple graph where the 

nodes are authors and the edges represent a coauthoring relationship. We can represent the same 

information using an affiliation network having a set of 

authors and a set of papers produced by those authors. 

If an author has written a paper, then there is a link 

between author and paper. We notice that we can still 

extract the information about co-authorships by examining the coauthors on all the papers that an author has 

produced. This operation of extracting a simple (or 

one-mode) network from an affiliation network is 

called a projection. 

A recent upsurge in affiliations research has followed from two observations. This first is that there 

are a large number of real-world networks that have a 

natural bipartite structure inherent in them. Affiliation 

networks are a natural way to capture this structure. 

Additionally, it has been shown that several desirable 

properties for models, seen in real-world networks, can 

be explained and captured by examining the changes to 

the affiliations associated with the networks. These 

properties include power-law distribution, small world 

properties, clustering, densification, and a shrinking 

diameter. It appears that understanding the affiliations 

associated with certain networks are necessary to be 

able to accurately model how those networks will 

evolve. 
 86 NIST Applied and Computational Mathematics Division 

B. Cloteaux and J. Shook are investigating methods to increase the accuracy of modeling using 

affiliation networks. Their approach uses probabilistic 

projections of the affiliation networks. A probabilistic 

projection is a projection where each edge has some 

probability of being included in the one-mode graph. 

The purpose behind using a probabilistic approach is to 

capture the idea that simply sharing an affiliation does 

not always translate into forming a relationship for 

entities in many real-world networks. The goal of this 

project is to create more realistic network models while 

preserving the advantages of creating these models 

using an affiliation approach.

ITL Program: Complex Systems

Degree-Based Modeling 

Brian D. Cloteaux 

During the past decade, there have been a number of 

papers devoted to describing the relationships between 

entities in a system using networks with power-law 

distributed degree sequences. In a network, the number 

of edges connected to a node is called the degree of the 

node and the set of all the degrees in a graph is called 

its degree distribution. For a degree sequence to be 

power-law distributed means that the probability that a 

node has k adjacent edges is P(k) ~ kα

 for some α > 1. 

This distribution in a graph produces a few nodes with 

very high degree (often called hub nodes) and a large 

number of low degree nodes. The importance of networks, especially those having power law distributions, 

for modeling applications lies in the number of areas in 

which they are found. These networks have been 

shown to arise naturally in systems of both biological 

and social interactions. They also appear in many engineered systems such as the power grid, the Internet, 

and software components. Thus, realistic models of 

these types of interactions need to reflect their powerlaw distribution. 

A usual first step in the creation of a model of a 

real-world complex network is to construct a graph 

with a given degree sequence. A problem rising from 

the random modeling of graphs is to generate a degree 

sequence from some given probability distribution. 

Specifically, the problem is assuring that the generated 

sequence can be realized by some graph. One approach, originally suggested by Mihail and Vishnoi [3], 

is to find the closest graphical sequence to a nongraphical integer sequence using a measure they call 

discrepancy. The discrepancy δ between two sequences, a and b, is given by the formula 



  

n

i

a b ai bi

1

( , )

While Mihail and Vishnoi did show an algorithm 

for this problem that is polynomial, their algorithm is 

far from optimal. B. Cloteaux has developed an algorithm [1], that runs in near-optimal time (linear time), 

for the determination of the closest graphical degree 

sequence in terms of discrepancy to a given nongraphical degree sequence. This result has been submitted to a journal, and a software implementation of 

the algorithm has been released [2]. 

[1] B. Cloteaux, Graphical Approximations of Degree Sequences, submitted. 

[2] http://www.nist.gov/itl/math/cctg/nmsw.cfm 

[3] M. Mihail, N. Vishnoi, On Generating Graphs with Prescribed Degree Sequences of Complex Network 

Modeling Applications, in Proceedings of the 3rd Workshop on Approximation and Randomization Algorithms 

in Communication Networks (ARACNE), pp. 1–11.

ITL Program: Complex Systems

Scaling of Congestion in Small 

World Networks 

Iraj Saniee (Alcatel-Lucent Bell Labs) 

Gabriel H. Tucci (Alcatel-Lucent Bell Labs) 

A remarkable and widely discussed phenomenon associated with networks in many applications is the small 

world property. It is observed in many such networks, 

man-made or natural, that the typical distance between 

the nodes is surprisingly small. More formally, as a 

function of the number of nodes, N, the average distance between a node pair typically scales at or below 

O(log(N)). In this work, we study the load characteristics of small world networks. Assuming one unit of 

demand between each node pair, we quantify as a function of N, how the maximal nodal load scales, 

independently of how each unit of demand may be 

Figure 44. A graph (top) and its associated affiliation network 

(bottom).
Summary of Activities for Fiscal Year 2011 87 

routed. In other words, we are interested in the smallest 

of such maximal nodal loads as a function of routing, 

which we refer to as congestion that the network could 

experience. 

We have shown that in planar small-world networks congestion is almost quadratic in N, which is as 

high as it can get, specifically O(N2

/log(N)). In contrast, for some non-planar small-world networks, 

congestion may be almost linear in N, namely O(N1+e) 

for arbitrarily small e. Since congestion in a network 

with N nodes cannot have scaling order less than O(N) 

or more than O(N2

), we conclude that the small world 

property alone is not sufficient to predict the level of 

congestion a priori and additional characteristics may 

be needed to explain congestion features of complex 

networks. 

Additionally, we investigate what happens to congestion when we change the link metric that prescribes 

routing. That is, for a network with edge weight {de}eE

we change the metric by a factor 0 ≤ we ≤ ∞ thus assigning each edge e a new weight wede. We explore the 

extent to which this change in the metric can change 

congestion in the network. We prove that if we allow 

the weights to get arbitrarily small or large, i.e., when 

for some edges, we approach zero and for some others 

we approach infinity, then considerable changes in 

congestion can occur. On the other hand, if we require 

the weights to be bounded away from zero and infinity, 

i.e. when 0 < k ≤ we ≤ K < ∞ for all edges e, then congestion cannot change significantly. These 

observations quantify the degree to which remetrization in a small world network may be helpful in 

affecting congestion. 

This work was performed at Alcatel-Lucent Bell 

Labs under a grant from NIST. 

[1] Iraj Saniee and Gabriel H. Tucci, Scaling of Congestion 

in Small World Networks, submitted. 

ITL Program: Complex Systems

Bootstrap Percolation on Random 

Geometric Graphs 

Milan Bradonjić (Alcatel-Lucent Bell Labs) 

Iraj Saniee (Alcatel-Lucent Bell Labs) 

Some crystals or lattices studied in physics and chemistry can be modeled as consisting of atoms occupying 

sites with specified probabilities. The lattice as a whole 

would then exhibit certain macroscopic properties, 

such as (ferro)magnetism, only when a sufficient number of neighboring sites of each atom are also similarly 

occupied. In computer memory arrays each functional 

memory unit can be considered as an occupied site, and 

a minimum percentage of functioning units are needed 

in the vicinity of each memory unit in order to maintain 

the array with proper functioning. In adoption of new 

technology or emergence of cultural fads, an individual 

is positively influenced when a sufficient number of its 

close friends have also done so. 

All three examples cited above may be modeled 

via a formal process called “bootstrap percolation,” 

which is a dynamic process that evolves similar to a 

cellular automaton. Unlike cellular automata, however, 

this process can be defined on arbitrary graphs and 

starts with random initial conditions. Vertices are either 

active or inactive. Once activated, a vertex remains 

active forever. Each vertex is initially active with a 

(given) probability p. Subsequently and at each (discrete) time step, a vertex becomes active if θ of its 

nearest neighbors are active, for a fixed value of θ = 1, 

2, 3 ... As time evolves, a fraction Φ of all the vertices 

are activated. The emergence of macroscopic properties of interest typically involve Φ to be at or close to 1. 

Many diffusion processes of interest have a physical contact element. A link in an ad hoc wireless 

network, a sensor network, or an epidemiological graph 

connotes physical proximity within a certain locality. 

Study of diffusion of virus spread in ad hoc wireless, 

sensor or epidemiological graphs requires this notion of 

neighborhood for accurate estimation of likelihood of 

full percolation. This is in contrast to models with 

long-range reach where physical proximity plays little, 

if any, role. The natural random model for such phenomena is the random geometric graph. In this work, 

we focus on bootstrap percolation on random geometric graphs, a topic that has not been investigated, to the 

best of our knowledge. We derive tight bounds on the 

critical threshold, pc, such that for all p > pc full percolation takes place. We conclude with simulations that 

compare numerical thresholds with those obtained analytically. 

This work was performed at Alcatel-Lucent Bell 

Labs under a grant from NIST. 

[1] Milan Bradonjić and Iraj Saniee, Bootstrap Percolation 

on Random Geometric Graphs, submitted. 

ITL Program: Complex Systems

Cross-layer Network Optimization 

for Diverse QoS Requirements 

Vladimir Marbukh 

Aggregate utility maximization as a goal for balancing competing user-level requirements was proposed in 

[1]. A distributed, price-based network utility maximization (NUM) framework for achieving this goal in a 

case when users express their utilities in terms of the 

end-to-end network bandwidth was developed in [2]. 
 88 NIST Applied and Computational Mathematics Division 

This framework assumes that elastic users respond to 

resource congestion prices represented by Lagrange 

multipliers associated with the capacity constraints. 

Later, NUM was extended to cross-layer optimization 

of wire-line as well as wireless networks [3,4]. These 

and other extensions retain the basic assumption of [2] 

that user utilities are expressed in terms of the end-toend bandwidth. 

However, typically it is more natural for users to 

quantify their preferences in terms of the high-level 

quality of service (QoS) parameters rather than lowlevel parameters such as end-to-end bandwidth, packet 

loss, etc. In [5] we suggest that the distributed, pricingbased framework [2,3,4] can be extended to this more 

general case by assuming that the user utilities are 

functions of both network and user level parameters, 

and the goal is to maximize the aggregate utility which 

is the sum of the individual user utilities. Replacing 

capacity constraints with constraints on the feasible 

QoS parameters may allow direct pricing of the QoS 

parameters in terms of the Lagrange multipliers associated with the QoS parameter constraints. 

To demonstrate flexibility of the proposed framework we consider two instances of QoS-sensitive 

utility maximization [5]. The first is end-to-end bandwidth allocation subject to the worst-case scenario endto-end delay. The allocation is based on generalized 

processor sharing (GPS) [6,7]. The second is end-toend bandwidth allocation subject to the average end-toend packet delay. This optimization framework relies 

on M/G/1 conservation laws for each link and assumes 

statistical independence of the queues on different links 

[8]. Both assume users sensitive to average transmission rate and end-to-end packet delays, which 

explicitly enter the user utility functions. 

The first instance is inherently simpler than the second since the worst-case scenario delay for GPScontrolled traffic is only determined by GPS parameters and does not depend on the packet-level traffic 

structure. The second instance yields an explicit solution for the QoS-sensitive traffic scheduling in a case 

of user utilities being linear with respect to the average 

end-to-end delays. The proposed cross-layer optimization increases the aggregate utility as compared to the 

conventional NUM by taking advantage of the heterogeneity of user QoS requirements. Possible extensions 

include optimization of non-linear user level utilities 

with respect to the average end-to-end delays. Generally, this optimization yields dynamic priority 

scheduling. A distributed user-level utility maximization should be based on direct pricing of QoS 

requirements, which includes numerous research issues. 

In our future work we plan to apply the proposed 

optimization technique to investigate architectural and 

methodological challenges of designing intelligent distributed systems capable of managing information 

assurance and security (IAS) related risks. We expect 

that system architecture should include sufficient intelligence enabling the system to assess and inform users 

on the IAS related risks, so that users would be able to 

select the acceptable level of risk according to their 

individual preferences. We intend to employ the relevant decision theory frameworks developed and 

successfully applied in economics and finance for IAS 

related risk assessment and management. 

[1] S. Shenker, Fundamental Design Issues for the Future 

Internet, IEEE Journal on Selected Areas in 

Communications 13 (1995), pp. 1176-1188. 

[2] F.P. Kelly, A.K. Maulloo, and D.H.K. Tan, The Rate 

Control for Communication Networks: Shadow Prices, 

Proportional Fairness and Stability, Journal of the 

Operations Research Society 409 (1998), pp. 237-252. 

[3] M. Chiang, Balancing Transport and Physical Layers in 

Wireless Multihop Networks: Jointly Optimal 

Congestion Control and Power Control, IEEE Journal 

on Selected Areas in Communications 23 (2005), pp. 

104-116. 

[4] X. Lin, N.B. Shroff, and R. Srikant, A Tutorial on 

Cross-Layer Optimization in Wireless Networks, IEEE 

Journal on Selected Areas in Communications 24(8) 

(2006), pp. 1452-1463. 

[5] V. Marbukh, Robust Cross-Layer Network Optimization 

for Diverse QoS Requirements: Work in Progress, in 

Proceedings of the 2011 World Congress on 

Engineering, London, U.K., July 6-8, 2011. 

[6] A.K. Parekh, R.G. Gallager, A Generalized Processor 

Sharing Approach to Flow Control in Integrated 

Services Networks: the Single-Node Case,” IEEE/ACM 

Transactions on Networking 1(3) (1993), pp. 344-357. 

[7] A.K. Parekh, R.G. Gallager, A Generalized Processor 

Sharing Approach to Flow Control in Integrated 

Services Networks: the Multiple-node Case,” 

IEEE/ACM Transactions on Networking 2(2) (1994), pp. 

137-150. 

[8] L. Kleinrock, Queueing Systems, Volume II: Computer 

Applications, John Willey, 1976. 

ITL Program: Complex Systems

Analysis of a Distributed Protocol 

for an Access Network with Multiple 

Users 

Fern Y. Hunt 

Vladimir Marbukh 

Congestion control is critical to the smooth functioning 

of modern communication networks in particular and 

the Internet in general. The goal of a congestion protocol is to allow many users to share network resources 

without overloading the system. In addition it is desirable to use as much of the available network capacity as 
Summary of Activities for Fiscal Year 2011 89 

possible and ensure some fairness in the allocation of 

bandwidth. It was shown by Frank Kelly and later 

many others that these objectives can be achieved by 

protocols that are based on solving a global optimization problem for maximizing system utility where some 

notion of fairness is expressed by a choice of utility 

function. The implication is that the operation of a protocol can be characterized and studied mathematically 

by analyzing the dynamics of an algorithm for solving 

the optimization problem. As the need for system robustness has grown amidst cyber security concerns, 

this paradigm has been extended to the problem of designing and characterizing protocols that control 

routing as well as congestion. 

Recently Hunt and Marbukh proposed a protocol 

[1] for allocating traffic that assigns routes randomly to 

users with prescribed path diversity. The entropy of the 

distribution of routes defined by an allocation is introduced in the corresponding utility maximization 

problem as a constraint so that users cannot use a single cheapest route as in the OSPF (open shortest path 

first) allocation. Introducing this feature reduces the 

risk of instability that arises in the unconstrained use of 

this protocol. In previous work on example networks 

with a single source and destination, e.g., [2], we 

showed that maximum utility could be achieved with 

an allocation of traffic that minimizes mean route cost. 

There we analyzed in detail the dynamics of the prices 

of constituent links that make up the routes. 

We have extended this work to a network topology 

with multiple and possibly large numbers of sources 

with a single destination. Such a topology could model 

multiple users (each associated with a source) accessing a single trunk line. Each source has two possible 

routes, a direct link to the destination and a second 

route that consists of a link connecting to its nearest 

neighbor followed by a direct route to the destination. 

Building on the analysis of a simple two-link network 

with a time constant route allocation, we examined the 

tradeoff between path diversity and utility in two situations. The first occurs when the capacities of all the 

direct links are equal to the same constant, with nearest 

neighbor links all having equal capacity (in general 

different from that of the direct links). By examining 

how utility varies with the route allocation entropy we 

identified conditions where the aggregate (or average) 

utility could be increased by increasing the amount of 

traffic on the indirect routes. Such off-loading of traffic 

can occur up to a critical value of the route allocation 

that depends on the link capacities. In the second case, 

the capacities of links are chosen to vary depending on 

the source the link is connected to. As in the previous 

case, each source has a critical value that determines 

the limit to which traffic can be transferred from direct 

to indirect routes. Here, that value differs for each 

source because it depends on the ratio of the capacities 

of the links attached to the source. Thus for some 

sources, individual source utility could benefit from 

offloading while the aggregate utility decreases, and 

the opposite could be true for other sources. 

[1] F.Y. Hunt, V. Marbukh, and Y. Wang, A Mathematical 

Model of Joint Congestion Control and Routing in Multisource Networks, in Proceedings of the 2011 IEEE 

International Conference on Control Applications, pp. 

1131-1138. 

[2] F.Y. Hunt and V. Marbukh, A Model of Joint Congestion Control and Routing Through Random Assignment 

of Paths, NISTIR 7590, February 2010.

ITL Program: Complex Systems

Methods that Streamline Search for 

Failure Scenarios in Large-Scale 

Systems 

Fern Y. Hunt 

Christopher Dabrowski (NIST ITL) 

Katherine Morrison (University of Nebraska–Lincoln) 

In recent years, the advent of large scale distributed 

systems such as computing grids and commercial cloud 

systems has made mass computing services available to 

populations of users on demand. These systems are 

dynamic, heterogeneous and—due to the interactions 

of its many components—subject to the emergence of 

unpredictable system wide behaviors that can have 

deleterious consequences. Their rapid growth and increasing economic importance underline the need for 

tools and methodologies that enable understanding and 

prediction of complex system behavior in order to insure the availability and reliability of these services. 

Key questions are the effect of changes in workload, 

system design and other operational parameters on 

overall system performance. For example, studies of 

alternative economic strategies and system failure scenarios have shown that small variations in key system 

parameters can lead to large differences in performance 

(see references in [1]). By large scale simulation we 

mean the discrete event simulations that simulate in 

detail the various stages encountered by an individual 

task over time. While the large scale simulations used 

in these studies are more practical than operational 

testbeds, computational expense rises dramatically with 

model size and number of tasks. This is a critical roadblock to extensive investigation of dynamical behavior 

in large scale systems. 

To address this situation, we introduced in earlier 

work [2], a succinct Markov chain representation of the 

dynamics of a large scale grid system over time. The 

chain simulates the progress of a large number of computing tasks from the time they are submitted by users 

to the time they either complete or fail. The evolution 
 90 NIST Applied and Computational Mathematics Division 

of the Markov chain itself occurs in discrete time 

through a set of transition probability matrices (TPMs). 

Each TPM simulates the grid system over a distinct 

time period and thus the Markov chain is piece-wise 

homogeneous. Changes in system parameters can be 

modeled by perturbing the TPMs of the Markov chain. 

The corresponding sample paths are altered and represent altered system execution paths that arise as a result 

of perturbed system parameters [2]. 

Through systematic perturbation of the TPM matrices followed by simulation of the resulting perturbed 

Markov chain we were able to identify scenarios that 

led to degradations of system performance and systemwide failure. Our results compared very favorably with 

large scale simulation results and were obtained with a 

substantial reduction in computational cost (hours vs. 

weeks of simulation). Nevertheless, as the number of 

states of the Markov chain grows, the computational 

cost of this method significantly increases. Thus it is 

very difficult to quickly identify the set of perturbed 

TPMs that lead to system deterioration or failure when 

the number of states is large. Prediction and ultimately 

control of these systems will depend on the ability to 

discover these scenarios quickly and perhaps in real 

time. This is the motivation of the work that is described in [1,2,3]. 

One approach is based on analyzing the underlying 

graph of the Markov chain. By efficiently identifying 

cut sets in the graph, system failure scenarios can be 

very rapidly identified. The method has been applied to 

grid systems, cloud systems, and to large energy systems as well. A second approach is based on the 

spectral properties of the Markov Chain. Our contribution here is two-fold. First, in the context of grid 

computing, we have developed a method for quickly 

generating the time course of a key variable of the system, the proportion of tasks completed for arbitrary 

system parameters, 

Second, we can measure the effect of perturbations 

on the spectral properties of the matrices associated 

with the Markov chain. Elevated levels of the quantities computed in the second method correlate well with 

deterioration in the number of tasks completed. We 

were able to identify all of the failure scenarios found 

by large scale simulation; however, the correlation is 

not perfect. In a small number of cases, elevated values 

occurred without any sign of a decrease in system performance. 

Nevertheless, we believe that these methodologies 

offer a promising first step toward the development 

ofscalable and efficient complex system monitoring 

and prediction. The use of Markov chains to approximate the dynamics of a variety of systems is well 

known. However, most of the applications involve the 

use of time homogeneous systems that reach steady 

state. The grid and cloud computing systems discussed 

here are both time inhomogeneous and absorbing. Thus 

much of the literature on perturbations of Markov 

chains does not apply. Papers describing the work on 

the spectral approach that appeared this year are [2] 

and [3]. The graph theory method is described in [1]. 

[1] C. Dabrowski and F. Hunt, Using Markov Chain and 

Graph Theory concepts to Analyze Behavior In Complex Distributed Systems, 23rd European Modeling & 

Simulation Symposium, September 2011. 

[2] C. Dabrowski and F. Hunt, Improving the Efficiency of 

Markov Chain Analysis of Complex Distributed Systems, NISTIR 7744, 2010.

[3] F. Hunt, C. Dabrowksi, and K. Morrison, Spectral Based 

Methods That Streamline the Search for Failure Scenarios in Large-Scale Distributed Systems, in Proceedings 

of the IASTED International Conference, Applied Simulation and Modeling (ASM 2011), June 2011. 

ITL Program: Complex Systems

Advanced Combinatorial Testing for 

Systems 

Raghu Kacker 

James Lawrence 

D. Richard Kuhn (NIST ITL) 

Yu (Jeff) Lei, University of Texas at Arlington 

Combinatorial testing (CT) is an approach to detect 

combinatorial interaction faults, which may cause a 

complex software based system to fail when some particular values of certain parameters combine with some 

particular values of certain other parameters. Many 

critical system failures in recent times have been traced 

to interaction faults in the underlying software. CT is a 

versatile and broadly applicable methodology for ensuring trustworthy software in business, industrial, 

medical, scientific, and transport systems. It is often 

difficult or impossible to characterize all possible combinatorial interactions, let alone test them. CT is based 

on the observation that most interaction faults involve 

only a few parameters. Several studies of actual faults 

show that most faults involved a single parameter, a 

smaller proportion of faults resulted from interactions 

between values of two parameters, and progressively 

fewer interaction faults involved 3, 4, 5, and 6 parameters. So far, a fault involving more than six parameters 

has not been seen. Most combinatorial testing has until 

recently been limited to pair-wise (2-way) testing in 

which all interactions involving two parameters are 

detected. A reason is that efficient test methods and 

tools to detect higher order interaction faults have so 

far not been available. The goal of this project is to 

advance the technology from pair-wise to higher order 

(strength) testing and to demonstrate successful applications of high strength combinatorial testing. 
Summary of Activities for Fiscal Year 2011 91 

We have made major revisions to the NIST/UTA 

software tool ACTS for generating high strength combinatorial test suites with constraints, distributed 950 

copies of ACTS worldwide, and approved redistribution within companies. We estimate the number 

of users of ACTS tool to be several thousand. We continue to provide consulting services upon request. 

Major ACTS Improvements made in 2011: 

1. Base-Choice Testing. This feature allows the user 

to designate a base value for each parameter. 

2. Test Output Specification. This feature allows the 

user to specify the expected output behavior for 

each test case. 

3. New Interface for Constraint Support. This new 

interface allows the user to free-type constraints. 

Significant validation support has also been added 

in the backend to ensure the legality of constraints 

before users enter into the test generation stage. 

4. API Interface. This feature allows the user to access the features of ACTS in a programmatic 

manner. 

5. Various Other Improvements. Better error handling, additional export formats, better mixedstrength support, and various GUI enhancements. 

Third-party Constraints Solver. We are investigating 

the use of a third-party constraints solver in ACTS for 

better and wider constraints support. We have developed a tool to determine “combinatorial coverage 

metrics” of candidate test suites. We have learned that 

determination of combinatorial coverage of existing 

test suites is in great demand. We have integrated the 

ACTS tool for software assurance into NIST’s Access 

Control Policy Test tool. 

Combinatorial Methods for Event Sequence Testing. Our discussions with the US Air Force 46-th Test 

Squadron led to understanding of a new testing problem: testing sequences of events. Some software 

testing problems involve sequences of events. For example, an embedded system may accept multiple 

sensor inputs and generate output to several communication links and effectors such as machine controls. It 

is important to test combinations of connected components, but also to test the order in which they could be 

connected. We have developed a methodology and 

prototype tools for generating test suites for sequential 

combinatorial testing. A paper submitted to IEEE 

Transactions on Software Engineering is being revised. 

Combinatorial-Based Prioritization for UserSession-Based Testing of Web. Our team has developed a prototype research tool labeled CPUT 

(Combinatorial-based Prioritization for User-sessionbased Testing) to convert web logs into user-sessionbased test suites so that testers can examine how users 

actually interact with the web application. Further, 

given that user-session-based test suites grow when 

many users access the system and testers may not be 

able to use all of the user-session-based test cases, 

CPUT provides functionality to prioritize these test 

suites by empirically verified criteria. CPUT allows 

researchers and practitioners to consider user-sessionbased testing and the respective prioritization techniques for their own projects. A paper on the tool was 

presented at the VERIFY/ATI Conference, September 

26, 2011, in Arlington, VA [5]. 

Publications. Our NIST Special Publication “Practical 

Combinatorial Testing,” issued in October 2010 [1], 

has been downloaded over 1,300 times already. We are 

planning to convert this publication into a published 

book. Our paper “A Combinatorial Approach to Detecting Buffer Overflow Vulnerabilities” [4] appeared 

in Proceedings of the 41st IEEE International Conference on Dependable Systems and Networks, Hong 

Kong, China, June 27-30, 2011. Our paper “A Survey 

of Binary Covering Arrays” [3] appeared in the Electronic Journal of Combinatorics. 

We have presented seminars and workshops on CT 

at a number of conferences. We are collaborating with 

the NASA Independent Verification and Validation 

(IV&V) facility to investigate use of CT in verification 

and validation of NASA software systems. 

[1] R. Kuhn, R. Kacker, and Y. Lei, Practical Combinatorial 

Testing, NIST Special Publication 800-142, October 

2010. 

[2] R. Kuhn, R. Kacker, and Y. Lei, Combinatorial Software Testing, LogiGear Magazine 4 (November 2010), 

San Mateo, CA. 

[3] J. Lawrence, R. Kacker, Y. Lei, D.R. Kuhn, and M. 

Forbes, A Survey of Binary Covering Arrays, Electronic 

Journal of Combinatorics 18 (2011), Article 84, 30 pgs. 

[4] W. Wang, Y. Lei, D. Liu, D. Kung, C. Csallner, D. 

Zhang, R. Kacker and R. Kuhn, A Combinatorial Approach to Detecting Buffer Overflow Vulnerabilities, in 

Proceedings of the 41st IEEE International Conference 

on Dependable Systems and Networks, Hong Kong, 

China, June 27-30, 2011, pp. 269-278. 

[5] S. Sampath, R. Bryce, S. Jain, S. Manchester, D.R. 

Kuhn (speaker), and R. Kacker, Practical Combinatorial 

Testing for Test Generation, VERIFY/ATI Conference, 

Arlington, VA, September 26, 2011. 
 92 NIST Applied and Computational Mathematics Division 

Security Risk Analysis of Enterprise 

Networks Using Attack Graphs 

Anoop Singhal (NIST/ITL) 

Su Zhang (Kansas State University) 

Xinming Ou (Kansas State University) 

John Homer (Abilene Christian University) 

http://csrc.nist.gov/groups/SNS/security-risk-analysisenterprise-networks/index.html

At present, computer networks constitute the core 

component of information technology infrastructures in 

areas such as power grids, financial data systems, and 

emergency communication systems. Protection of these 

networks from malicious intrusions is critical to the 

economy and security of our nation. Vulnerabilities are 

regularly discovered in software applications which are 

exploited to stage cyber attacks. Currently, management of security risk of an enterprise network is more 

an art than a science. System administrators operate by 

instinct and experience rather than relying on objective 

metrics to guide and justify decision making. The objective of this research is to develop a standard model 

for measuring the security of computer networks. A 

standard model will enable us to answer questions such 

as, “Are we more secure now than yesterday?”, or 

“How does the security of one network configuration 

compare with another one?” Also, having a standard 

model to measure network security will allow users, 

vendors and researchers to evaluate methodologies and 

products for network security in a coherent and consistent manner. 

We have approached the challenge of network security analysis by capturing vulnerability 

interdependencies and measuring security in the exact 

way that real attackers penetrate the network. Our 

methodology for security risk analysis is based on the 

model of attack graphs. We analyze all attack paths 

through a network, providing a probabilistic metric of 

the overall system risk. Through this metric, we analyze trade-offs between security costs and security 

benefits. 

In FY 2011, we worked on validating our approach for realistic networks. We used a real network 

as a test bed to demonstrate the utility of this approach. 

The results of our experiments were published in the 

Proceedings of the 2011 World Congress in Computer 

Science, Special Track on Security and Mission Assurance [1]. We have also documented our methodology 

and the results of our experiments in a NIST report [2]. 

In FY 2012 we plan to integrate our techniques into 

existing attack graph-based security tools. 

This work was performed in the NIST Computer 

Security Division with partial support from ACMD. 

[1] S. Zhang, X. Ou, A. Singhal, and J. Homer, An Empirical Study of a Vulnerability Aggregation Method, in 

Proceedings of the 2011 World Congress in Computer 

Science, Special Track on Security and Mission Assurance, Las Vegas, July 2011. 

[2] A. Singhal and X. Ou, Security Risk Analysis of Enterprise Networks Using Probabilistic Attack Graphs, 

NISTIR 7788, September 2011. 

Mobile Sensor Networks 

Vladimir Marbukh 

Kamran Sayrafian-Pour (ITL) 

Hamid Mahboubi (Concordia University) 

Kaveh Moezzi (Concordia University) 

Amir G. Aghdam (Concordia University) 

Mobile sensor networks (MSN) are envisioned to offer 

a novel set of applications in detecting, monitoring and 

tracking people, targets or events in pervasive computing environments [1]. Locations of sensors in a MSN 

affect both their ability to acquire information on the 

intended target(s) and event(s) as well as their ability to 

communicate this information to the intended recipient(s). The information acquisition needs, which 

require proximity to the target(s), often compete with 

the communication needs, which require proximity to 

the recipient(s) of the sensor information. Inherent 

traits of MSN such as lack of centralized control, variety of performance criteria, operational uncertainties, 

and possibilities of MSN topology change and sensor 

trapping in suboptimal locations make MSN optimization an exceedingly challenging problem. 

Our previous publications [2]-[5] have proposed 

aligning sensor mobility with the overall MSN goals by 

assuming that (a) sensing and communication are optimized much faster than sensors relocation and (b) 

sensor relocations are governed by cost/benefit analysis, where the “cost” of sensor battery energy 

expenditure for sensor relocation is weighted against 

projected performance gains due to new sensor locations. This approach is superior to sensor mobility 

control based on phenomenologically defined potential 

fields and the corresponding virtual forces [6], since 

dissipation of the non-renewable sensor battery energy, 

asymmetric virtual forces due to asymmetric wireless 

channels, and abrupt changes in the optimal MSN topology with sensor relocation are inconsistent with the 

existence of a global potential field. 

Practicality of the framework proposed in [2]-[5] 

depends on overcoming numerous challenges with the 

(inherently) distributed nature of MSN being the most 

critical. An intelligent sensor may have direct 

knowledge of its current life expectancy, as determined 

by its battery energy level and depletion rate affected 

by the surrounding terrain, as well as sensor infor-
Summary of Activities for Fiscal Year 2011 93 

mation acquisition and transmission capabilities. 

However, a sensor typically has no direct knowledge of 

the effect of its relocation on the rest of the MSN. 

Our paper [7] suggests that the class of distributed 

subgradient projection algorithms (DSPA) [8]-[9] has 

potential for addressing major challenges of controlled 

sensor mobility in MSN. Subgradient-based iterations 

allow for dynamic network topology optimization. Projection of the algorithm iterations onto the set of 

feasible sensor locations ensures sensor information 

acquisition and communication needs. Most importantly, communication overhead reducing techniques allow 

for addressing the inherently distributed nature of 

MSN. While more conventional pricing-based algorithms effectively reduce the communication overhead 

in some particular situations, recently emerged consensus-based algorithms have low communication 

overhead in a more general setting. 

Consensus-based algorithms differ in their approach to achieving consensus. In the first type, each 

agent maintains and iterates its own sequence, and consensus is achieved by communicating this sequence to 

the neighboring nodes, which incorporate neighbors’ 

sequences into their own sequences through averaging. 

In the second type, all agents update a single sequence, 

and consensus is achieved by passing the sequence 

instances to each other. In [7] we concentrated on the 

first type, since updating and passing instances of a 

single sequence by agents to each other exposes algorithms to the risk of manipulation by malicious agents, 

while averaging with judiciously chosen weights can 

mitigate this risk. 

A major difficulty with controlling sensor relocation is the possibility of sensor trapping in suboptimal 

locations (e.g. in non-flat terrain) due to typical nonconvexity of the performance criterion [8]. A possible 

approach to overcoming this difficulty is allowing occasional random sensor relocations to escape the 

potential traps in the spirit of a simulated annealing 

optimization algorithm. One of the advantages of this 

approach [7] is in its ability to incorporate such random 

moves in a distributed way. Initial simulation results 

indicate the viability of this approach for prolonging 

the MSN life-span. 

Future research should evaluate the pros and cons 

of different versions of distributed subgradient algorithms with respect to controlled sensor relocation, and 

provide guidelines for selection of the algorithm step 

size and free parameters involved in the “consensus” 

step. These selections affect the trade-off between the 

algorithm convergence rate and communication overhead. The ability to avoid traps on non-flat terrains is 

critical for practical implementation of controlled sensor relocation. Paper [7] suggests the possibility of 

achieving this by combining distributed subgradient 

projection and simulated annealing algorithms. 

More studies are needed to realize this possibility 

and compare algorithm [7] with more conventional 

optimization algorithms [9]. Paper [9] is concerned 

with target monitoring using a network of collaborative 

mobile sensors. The objective is to compute (online) 

the desired sensing and communication radii of sensors 

as well as their location at each time instant, such that a 

set of prescribed specifications are met. These specifications include end-to-end connectivity preservation 

from the target to a fixed destination, while durability 

of sensors is maximized and the overall energy consumption is minimized. The problem is formulated as a 

constrained optimization, and a procedure is presented 

to solve it. Simulation results demonstrate the effectiveness of the proposed techniques. 

In papers [10]-[11] various sensor deployment 

strategies are studied for effective coverage in wireless 

sensor networks. In [10], efficient sensor deployment 

algorithms are proposed to improve the coverage area 

in the target field. The proposed algorithms calculate 

the position of the sensors iteratively based on the existing coverage holes in the target field. The 

multiplicatively weighted Voronoi diagram (MWVoronoi diagram) is used to discover the coverage 

holes corresponding to different sensors with different 

sensing ranges. Under the proposed procedures, the 

sensors move in such a way that the coverage holes in 

the target field are reduced. Simulation results are provided to demonstrate the effectiveness of the 

deployment schemes proposed in this paper. 

The algorithms proposed in [11] consider the distances of each sensor and the points inside its 

corresponding Voronoi polygon from the edges or vertices of the polygon. Four algorithms are developed: 

Maxmin-vertex, Maxmin-edge, Minmax-edge, and a 

hybrid algorithm. The main characteristic of these algorithms is the iterative movement of the sensors. Once 

each destination is computed, the new local coverage 

area of the corresponding sensor is compared with its 

previous local coverage area. If the new local coverage 

area is larger than the preceding one, the sensor moves 

to the new destination; otherwise, it remains in its current location. If, on the other hand, the local coverage 

area by none of the sensors is improved by a certain 

threshold, then the iteration stops. This termination 

condition guarantees that the proposed algorithms arrive at the desired destination (with a prescribed 

accuracy which is set by the above-mentioned threshold level) in finite time. The proposed strategies 

outperform the existing ones in the case when some 

sensors are required to move toward sharp vertices. 

[1] I.F. Akyildiz, W Su, Y. Sankarasubramanian, and E. 

Cayirci, Wireless Sensor Networks: A Survey, 

Computer Networks 32 (2002), pp. 393-422. 

[2] V. Marbukh and K. Sayrafian-Pour, A Framework for 

Joint Cross-Layer and Node Location Optimization in 
 94 NIST Applied and Computational Mathematics Division 

Mobile Sensor Networks, in Proceedings of AdhocNow’09, Nice, France, 2008. 

[3] V. Marbukh and K. Sayrafian-Pour, Mobile Sensor 

Network Self-Organization for System Utility 

Maximization: Work in Progress, in Proceedings of the 

Fifth International Conference on Wireless and Mobile 

Communications (ICWMC’09), Cannes 2009. 

[4] H. Mahboubi, A. Momeni, A. G. Aghdama, K. 

Sayrafian-Pour, and V. Marbukh, Minimum Cost 

Routing with Controlled Node Mobility for Target 

Tracking in Mobile Sensor Networks, 2010 American 

Control Conference (ACC2010), USA, 2010. 

[5] V. Marbukh, K. Sayrafian-Pour, H. Mahboubi, A. 

Momeni, and A.G. Aghdam, Towards EvolutionaryPricing Framework for Mobile Sensor Network SelfOrganization, in Proceedings of 2010 IEEE World 

Congress on Computational Intelligence, Barcelona, 

Spain, 2010. 

[6] A. Howard, M.J. Mataric, and G.S. Sukhatme, Mobile 

Sensor Network Deployment using Potential Fields: a 

Distributed, Scalable Solution to the Area Coverage 

Problem, in Proceedings of the 6th International 

Symposium on Distributed Autonomic Robotic Systems 

(DARS’02), Fukuoka, Japan, 2002. 

[7] V. Marbukh, K. Sayrafian-Pour, H. Mahboubi, A. 

Momeni, and A.G. Aghdam, Cooperative Sensor 

Relocation in a Mobile Sensor Network by Distributed 

Subgradient Algorithm, SENSOCOMM 2011, Nice, 

France, Aug. 21-26, 2011. 

[8] Y. Koren and J. Borenstein, Potential Field Methods and 

their Inherent Limitations for Mobile Robot Navigation, 

in Proceedings of the IEEE Conference on Robotics and 

Automation, Sacramento, California, April 7-12, 1991, 

pp. 1398-1404. 

[9] H. Mahboubi, A. Momeni, A. Aghdam, K. Sayrafian, 

and V. Marbukh, An Efficient Target Monitoring 

Scheme with Controlled Node Mobility for Sensor 

Networks, IEEE Transactions on Control Systems 

Technology, accepted.. 

[10] K. Sayrafian-Pour, H. Mahboubi, K. Moezzi, and A.G. 

Aghdam, and V. Marbukh, Self-Deployment Algorithms 

for Coverage Problem in a Network of Mobile Sensors 

with Un-identical Sensing Range, in Proceedings of the

IEEE Global Communications Conference

(GLOBECOM 2010), Miami, USA, December 2010. 

[11] K. Sayrafian-Pour, H. Mahboubi, K. Moezzi, A.G. 

Aghdam, and V. Marbukh, Distributed Deployment 

Algorithms for Improved Coverage in Mobile Sensor 

Networks, in Proceedings of the 2011 IEEE Multiconference on Systems and Control (MSC 2011),

Denver, Colorado, USA, September 28-30, 2011. 

ITL Program: Pervasive Information Systems
Summary of Activities for Fiscal Year 2011 95 

Part IV: Activity Data 

 Part IV

 Activity Data 
 96 NIST Applied and Computational Mathematics Division 
Summary of Activities for Fiscal Year 2011 97 

Publications 

Appeared 

Refereed Journals 

1. J. D. Benson, A. Bagchi, X. Han, J. K. Critser, E. 

J. Woods, Melting Point Equations for the Ternary 

System Water-sodium Chloride-ethylene Glycol 

Revisited, Cryobiology 61 (3) (Dec. 2010), pp. 

352-356. 

2. K. R. Brown, A. C. Wilson, Y. Colombe, C. Ospelkaus, A. M. Meier, E. Knill, D. Leibfried, and 

D. J. Wineland, Single-Qubit-Gate Error Below 

10-4 in a Trapped Ion, Physical Review A 84

(2011), Article 030303(R), 4 pgs. 

3. T. J. Burns, S. P. Mates, R. L. Rhorer, E. P. 

Whitenton, and D. Basak, Dynamic Properties for 

Modeling and Simulation of Machining: Effect of 

Pearlite to Austenite Phase Transition on Flow 

Stress in AISI 1075 Steel, Machining Science & 

Technology 15 (1) (Jan. 2011), pp. 1–20.

4. B. Cloteaux and N. Serova, Matching Observed 

Alpha Helix Lengths to Predicted Secondary 

Structure, International Journal of Computational 

Bioscience 1 (2010), pp. 103-110.

5. B. Cloteaux, Approximating the Number of Bases 

for Almost All Matroids, Congressus Numerantium 202 (2010), pp. 149-154.

6. H. S. Cohl, On Parameter Differentiation for Integral Representations of Associated Legendre 

Functions, Symmetry, Integrability, and Geometry: 

Methods and Applications 7 (050) (2011), 16 pgs. 

7. H. S. Cohl, Generalized Heine’s Identity for Complex Fourier Series of Binomials, in Proceedings 

of the Royal Society A 467 (February 2011), pp. 

333-345. 

8. H. S. Cohl, Fundamental Solution of Laplace's 

Equation in Hyperspherical Geometry, Symmetry, 

Integrability, and Geometry: Methods and Applications 7 (108) (2011), 14 pgs. 

9. A. A. Dima, J. T. Elliott, J. J. Filliben, M. Halter, 

A. Peskin, J. Bernal, B. L. Stottrup, M. Kociolek, 

M. C. Brady, H. C. Tang, and A. L. Plant, Comparison of Segmentation Algorithms for 

Flourescence Microscopy Images of Cells, Cytometry Part A 79A (2011), pp. 545-559. 

10. R. D. Johnson, III, K. K. Irikura, R. Kacker, and R. 

Kessel, Response to Comment on ‘Uncertainty in 

Scaling Factors for ab Initio Vibrational Zeropoint Energies’ and ‘Calibration Sets and the Accuracy of Vibrational Scaling Factors: A Case 

Study with the X3LYP Hybrid Functional, Journal of Chemical Physics 134 (2011), Article 

167102, 2 pgs.. 

11. R. Kacker and J. Lawrence, Derivation of Isosceles Trapezoidal Distributions, Measurement 

Science and Technology 22 (2010), pp. 015106-

015111. 

12. J. Lawrence, R. Kacker, Y. Lei, D.R. Kuhn, and 

M. Forbes, A Survey of Binary Covering Arrays, 

Electronic Journal of Combinatorics 18 (2011), 

Article 84, 30 pgs. 

13. L. Ma, J. C. Bienfang, O. Slattery, and X. Tang, 

Up-conversion Single-photon Detector Using Multi-wavelength Sampling Techniques, Optics 

Express 19 (6) (March 14, 2011) pp. 5470-5479. 

14. L. Ma, M. T. Rakher, M. J. Stevens, O. Slattery, 

K. Srinivasan, and X. Tang, Temporal Correlation 

of Photons Following Frequency UpConversion, Optics Express 19 (11) (May 23, 

2011), pp. 10501-10510. 

15. F. Mallet, M. A. Castellanos-Beltran, H. S. Ku, S. 

Glancy, E. Knill, K. D. Irwin, G. C. Hilton, L. R. 

Vale, and K. W. Lehnert. Quantum State Tomography of an Itinerant Squeezed Microwave Field, 

Physical Review Letters 106 (2011), Article 

220502. 

16. N. S. Martys, W. L. George, B.-W. Chun, D. Lootens, A Smoothed Particle Hydrodynamics Based 

Fluid Model with a Spatially Dependent Viscosity: 

Application to Flow of a Suspension with a NonNewtonian Fluid Matrix, Rheologica Acta 49 (10) 

(2010), pp. 1059-1069. 

17. G. B. McFadden, S. R. Coriell, and P. A. Lott, 

Onset of Morphological Instability in Two Binary 

Liquid Layers, Physics of Fluids 23 (4) (April 

2011), Article 044102, 8 pgs. 

18. M. T. Rakher, L. Ma, O. Slattery, X. Tang and K. 

Srinivasan, Quantum Transduction of Telecommunications-band Single Photons From a 

Quantum Dot by Frequency Upconversion, Nature 

Photonics 4 (Oct. 3, 2010), pp. 786-791. 

19. M. T. Rakher, L. Ma, M. Davanço, O. Slattery, X. 

Tang, and K. Srinivasan, Simultaneous Wavelength Translation and Amplitude Modulation of 

Single Photons from a Quantum Dot, Physical Review Letters 107 (Aug. 19, 2011), Article 083602. 

20. B. W. Rust, A Mathematical Model of Atmospheric Retention of Man-made CO2 Emissions, 

Mathematics and Computers in Simulation 81

(2011), pp. 2326-2336. 
 98 NIST Applied and Computational Mathematics Division 

21. K. Sayrafian-Pour, W.-B. Yang, J. Hagedorn, J. 

Terrill, K. Y. Yazdandoost, and K. Hamaguchi, 

Channel Models for Medical Implant Communication, International Journal of Wireless Information 

Networks 17 (3-4) (December 2010), pp. 105-112. 

22. J. S. Sims and S. A. Hagstrom, Hylleraasconfiguration-interaction Study of the Singlet S 

Ground State of Neutral Beryllium, Physical Review A: Atomic, Molecular, and Optical Physics

83 (2011), 032518. 

Journal of Research of NIST 

1. R. N. Kacker, R. Kessel, and K.-D. Sommer, Assessing Differences Between Results Determined 

According to the Guide to the Expression of Uncertainty in Measurement, Journal of Research of 

the NIST 115 (6) (November-December 2010), pp. 

453-459. 

2. Z. H. Levine, B. R. Galloway, and A. P. Peskin, 

RECIST Applied to Realistic Tumor Models, 

Journal of Research of the NIST 116 (3) (MayJune 2011), pp. 685-688. 

3. J. C. Wu, A. F. Martin, and R. N. Kacker,

Measures, Uncertainties, and Significance Test in 

Operational ROC Analysis, Journal of Research of 

the NIST, 116 (1) (2011), pp. 517-537. 

Book Chapters 

1. L. Ma, O. Slattery, and X. Tang, Single Photon 

Detection Using Frequency Up-Conversion with 

Pulse Pumping, in Photodiodes – Communications, Bio-Sensings, Measurements and HighEnergy Physics (J.-W. Shi, ed.), InTech, September 2011, pp. 61-76. 

2. A. Mink, L. Ma, B. Hershman, and X. Tang, An 

Application of Quantum Networks for Secure Video Surveillance, in Video Surveillance (W. Lin, 

ed.), InTech, February 2011, pp. 73-98. 

Conference Proceedings 

1. D. Banerjee, E. Simiu, J. Gross, and R. Kacker, A 

Statistical Analysis of Steel Truss Temperature 

Data Recorded During Fire Resistance Tests, in 

Proceedings of the 11th International Conference 

on Applications of Statistics and Probability in 

Civil Engineering (Faber, Kohler and Nishijima, 

eds.), ETH, Zurich, Switzerland, August 1-5, 

2011, pp. 960-965. 

2. T. J. Burns, S. P. Mates, R. L. Rhorer, E. P. 

Whitenton, and D. Basak, On Modeling the Peak 

Temperature on the Tool-chip Interface During 

High-speed Machining of AISI 1045 Steel, in 

Proceedings of the Eighth International Conference on High-Speed Machining, Metz, France, 

December 8-10, 2010. 

3. T. J. Burns, S. P. Mates, R. L. Rhorer, E. P. 

Whitenton, D. Basak, Effect on Flow Stress of a 

Rapid Phase Transition in AISI 1045 Steel, in 

Proceedings of the ASME 2011 International 

Manufacturing Science and Engineering Conference, Corvallis, OR, June 13-17, 2011. 

4. J. Chalfoun, A. Dima, A.P. Peskin, J. Elliott, J.J. 

Filliben, A Human Inspired Local Ratio-Based 

Algorithm for Edge Detection in Fluorescent Cell 

Images, in Proceedings of the 6th International 

Symposium on Visual Computing 2010 (G. Bebis 

et al., eds.), Part I, Lecture Notes in Computer Science 6453, Springer, Heidelberg (2010), pp. 23-34. 

5. B. Cloteaux, Modeling Affiliations in Networks, in 

Proceedings of the Winter Simulation Conference, 

Baltimore, MD, December 5-8, 2010, pp. 2958-

2967. 

6. C. Dabrowski and F. Hunt, Using Markov Chain 

and Graph Theory Concepts to Analyze Behavior 

in Complex Distriubuted Systems, in Proceedings 

of the 23rd European Modeling & Simulation 

Symposium, Rome, Italy, September 12-14, 2011. 

7. D. Duthinh and F. Potra, Probabilistic and Optimization Considerations in Multihazard Engineering, 

in Vulnerability, Uncertainty, and Risk: Analysis, 

Modeling, and Management, Proceedings of the 

ICVRAM 2011 and ISUMA 2011 Conferences, 

American Society of Civil Engineers, 2011. 

8. D. Ginev, H. Stammerjohanns, B. Miller, and M. 

Kohlhase, The LaTeXML Daemon: Editable Math 

on the Collaborative Web, in Proceedings of Conference on Intelligent Computer Mathematics, 

Bertinoro, (J. Davenport, et al., eds), Lecture 

Notes in Computer Science 6824, Springer, Heidelberg (2011), pp. 292-294. 

9. T. Gerrits, S. Glancy and S. W. Nam, A Balanced 

Homodyne Detector and Local Oscillator Shaping 

for Measuring Optical Schrödinger Cat States, in 

Proceedings of SPIE 8033, Advanced Photon 

Counting Techniques V (M. A. Itzler and J. C. 

Campbell, eds.), (April 2011), Article 80330X. 

10. T. Gerrits, B. Baek, M. Stevens, B. Calkins, A. 

Lita, S. Glancy, E. Knill, S.W. Nam, R. Mirin, R. 

Hadfield, R. Bennink, W. Grice, S. Dorenbos, T. 

Zijlstra, T. Klapwijk, and V. Zwiller, Characterization of High-purity, Pulsed Squeezed Light at 

Telecom Wavelengths from pp-KTP for Quantum 

Information Applications, in Proceedings of 
Summary of Activities for Fiscal Year 2011 99 

CLEO: QUELS 2011, Baltimore, MD, May 1-6, 

2011. 

11. F. Y. Hunt, K. Morrison, and C. Dabrowski, Spectral Based Methods That Streamline the Search for 

Failure Scenarios in Large-Scale Distributed Systems, in Proceedings of the IASTED International 

Conference, Applied Simulation and Modeling 

(ASM 2011), Crete, Greece, June 22-24, 2011, pp. 

109-116. 

12. F. Y. Hunt, V. Marbukh, and Y. Wang, A 

Mathematical Model of Joint Congestion Control 

and Routing in Multisource Networks, in 

Proceedings of the 2011 IEEE International 

Conference on Control Applications, Denver , CO, 

September 28-30, 2011. 

13. L. Ma, J. C. Bienfang, O. Slattery, and X. Tang, 

Up-conversion Single-photon Detectors for Quantum Communication Systems, in Proceedings of

SPIE 8033, Advanced Photon Counting Techniques V (M. A. Itzler and J. C. Campbell, eds.),

(April 2011), Article 803306.

14. L. Ma, J. C. Bienfang, O. Slattery, and X. Tang, 

Multi-wavelength Pumping Techniques for Upconversion Single-photon Detectors ,in Proceedings of CLEO: QUELS 2011, Baltimore, MD, May 

1-6, 2011.

15. L. Ma, M. T. Rakher, M. J. Stevens, O. Slattery, 

K. Srinivasan, and X. Tang, Preservation of Highorder Photon Correlations Following Frequency 

Up-conversion, in Proceedings of Nonlinear Optics, ISOM/ODS, Kauai, HI, July 17-20, 2011. 

16. L. Ma, O. Slattery, and X. Tang, Single Photon 

Frequency Up-conversion and Its Applications, in 

Proceedings of SPIE 8163 (Sept. 2011), Quantum 

information and Quantum Technology I (Ronald 

E. Meyers, Yanhua Shih, Keith S. Deacon (eds.), 

Article 81630N. 

17. V. Marbukh, A.G. Aghdama, H. Mahboubi, A. 

Momeni, and K. Sayrafian-Pour, Self-deployment 

Algorithms for Coverage Problem in a Network of 

Mobile Sensors with Un-identical Sensing Ranges, 

in Proceedings of IEEE Globecom 2010, Miami, 

FL, December 6-10, 2010. 

18. V. Marbukh, Robust Cross-layer Network Optimization for Diverse QoS Requirements: Work in 

Progress, in Proceedings of the 2011 International 

Conference of Applied and Engineering Mathematics, London, UK, July 6-8, 2011. 

19. V. Marbukh, Towards Modeling Effect of Multiscale Stochastic Dynamics on Flow-Level 

Queuing Performance in the Internet, in Proceedings of the 7th International Congress on 

Industrial and Applied Mathematics (ICIAM 

2011), Vancouver, Canada, July 18-22, 2011. 

20. V. Marbukh, K. Sayrafian-Pour, H. Mahboubi, A. 

Momeni, and A. G. Aghdam, Cooperative Sensor 

Relocation in a Mobile Sensor Network by Distributed Subgradient Algorithm, in Proceedings of 

SENSOCOMM 2011, Nice, France, August 20-25, 

2011. 

21. V. Marbukh, K. Sayrafian-Pour, H. Mahboubi, K. 

Moezzi, and A. G. Aghdam, Distributed Deployment Algorithms for Improved Coverage in 

Mobile Sensor Networks, in Proceedings of the 

2011 IEEE Multi-conference on Systems and Control, Denver , CO, September 28-30, 2011.

22. W. F. Mitchell and M. A. McClain, A Survey of 

hp-Adaptive Strategies for Elliptic Partial Differential Equations, in Recent Advances in 

Computational and Applied Mathematics (T. E. 

Simos, ed.), Springer, 2011, pp. 227-258. 

23. J. S. Pelc, C. R. Phillips, C. Langrock, Q. Zhang, 

L. Ma, O. Slattery, X. Tang, and M. M. Fejer, Single-Photon Detection at 1550 nm via 

Upconversion Using a Tunable Long-Wavelength 

Pump Source, in Proceedings of CLEO: QUELS 

2011, Baltimore, MD, May 1-6, 2011. 

24. A. Peskin and A. Dima, Modeling Clinical Tumors 

to Create Reference Data for Tumor Volume 

Measurement, in Proceedings of the 6th International Symposium on Visual Computing 2010 (G. 

Bebis et al., eds.), Part II, Lecture Notes in Computer Science 6454, Springer, Heidelberg (2010), 

pp. 736-746. 

25. A. Peskin, A. Dima, J. Calfoun, J. Elliott, Predicting Segmentation Accuracy for Biological Cell 

Images, in Proceedings of the 6th International 

Symposium on Visual Computing 2010 (G. Bebis 

et al. eds.), Part I, Lecture Notes in Computer Science 6453, Springer, Heidelberg (2010), pp. 549-

560. 

26. A. P. Peskin, D. J. Hoeppner, and C. H. Stuelten, 

Segmentation and Cell Tracking of Breast Cancer 

Cells, in Proceedings of the 7th International 

Symposium on Visual Computing, (G. Bebis et al., 

eds.), Part I, Lecture Notes in Computer Science 

6938, Springer, Heidelberg (2011), pp. 381-391. 

27. M. T. Rakher, L. Ma, O. Slattery, X. Tang, and K. 

Srinivasan, Quantum Transduction of Telecommunications-band Single Photons from a Quantum 

Dot by Frequency Upconversion, in Proceedings 

of Frontiers in Optics 2010, October 24-28, 2010, 

Rochester, New York. 
 100 NIST Applied and Computational Mathematics Division 

28. M. Stevens, S. Glancy, S. W. Nam, and R. Mirin, 

Third-Order Antibunching from an Imperfect Single-Photon Source, in Proceedings of CLEO: 

QUELS 2011, Baltimore, MD, May 1-6, 2011. 

29. D. Swanson and J. T. Fong, A High-Risk HighReward Approach to Public-Private Collaborative 

Research in Predictive Modeling & Control of 

Complex Systems, in Proceedings 2011 ASME 

Pressure Vessels and Piping Division Conference, 

Baltimore, MD, July 17-22, 2011, Article 

PVP2011-57712 (2011). 

30. X. Tang, L. Ma and O. Slattery, Ultra Low Darkcount-rate Up-conversion Single Photon Detector, 

in Proceedings of the IEEE Photonics Society 23rd

Annual Meeting, Denver CO, November 7-11, 

2010. 

31. W. Wang, Y. Lei, D. Liu, D. Kung, C. Csallner, D. 

Zhang, R. Kacker and R. Kuhn, A Combinatorial 

Approach to Detecting Buffer Overflow Vulnerabilities, in Proceedings of the 41st IEEE 

International Conference on Dependable Systems 

and Networks, Hong Kong, China. June 27-30, 

2011, pp. 269-278. 

32. J. C. Wu, A. Martin, C. Greenberg, and R. Kacker, 

Uncertainties of Measures in Speaker Recognition 

Evaluation, in Proceedings of the SPIE 8040, Defense, Security, and Sensing Conference, Orlando, 

FL, April 25-29, 2011, Article 804008. 

33. W.-B. Yang, K. Sayrafian-Pour, J. Hagedorn, J. 

Terrill, K. Y. Yazdandoost, A. Taparugssanagorn, 

M. Hamalainen, and J. Iinatti, Impact of an Aortic 

Valve Implant on Body Surface UWB Propagation: A Preliminary Study, in Proceedings of the 

Fifth International Symposium on Medical Information and Communication Technology (ISMICT), 

Montreux, Switzerland, March 27-31, 2011. 

Sponsored Research 

34. S. Zhang, X. Ou, A. Singhal, and J. Homer, An 

Empirical Study of a Vulnerability Aggregation 

Method, in Proceedings of the 2011 World Congress in Computer Science, Special Track on 

Security and Mission Assurance, Las Vegas, July 

2011. [NIST Computer Security Division]

Technical Magazine Articles 

1. I. Beichl, Changes, Computing in Science & Engineering 13 (1) (January 2011), p. 4. 

2. I. Beichl, Watchful Waiting, Computing in Science 

& Engineering 13 (2) (March 2011), pp. 3-4. 

3. I. Beichl, Dystopia, Computing in Science & Engineering 12 (6) (June 2011), p. 4. 

4. I. Beichl, Top of the Charts, Computing in Science 

& Engineering 13 (5) (September 2011), p. 4. 

5. R. Boisvert, C. W. Clark, D. Lozier and F. Olver, 

A Special Functions Handbook for the Digital 

Age, Notices of the American Mathematical Society 58 (7) (August 2011), pp. 905-911 and 928. 

6. J. W. Bullard, E. J. Garboczi, W. L. George, N. S. 

Martys, S. G. Satterfield, and J. E. Terrill, Advancing the Materials Science of Concrete with 

Supercomputers, Concrete Internationa1 33 (1) 

(January 2011), pp. 24-29. 

7. T. J. Hewison and R. Kessel, Common Reference 

Channels for Metrological Comparability, Global 

Space-based Inter-Calibration System (GSICS) 

Quarterly 4 (4) (December 2010). 

8. R. Kessel and T. J. Hewison, Defining Common 

Reference Channels for Geostationary Infrared 

Imagers, Global Space-based Inter-Calibration 

System (GSICS) Quarterly 4 (4) (December 2010). 

9. R. Kuhn, R. Kacker, and Y. Lei, Combinatorial 

Software Testing, LogiGear Magazine 4 (November 2010), San Mateo, CA. 

Technical Reports 

1. C. Dabrowski, F. Hunt, and K. Morrison, Improving Efficiency of Markov Chain Analysis of 

Complex Distributed Systems, NISTIR 7744, November 2010. 

2. R. Kuhn, R. Kacker, and Y. Lei, Practical Combinatorial Testing, NIST Special Publication 800-

142, October 2010. 

Sponsored Research 

3. A. Singhal and X. Ou, Security Risk Analysis of 

Enterprise Networks Using Probabilistic Attack 

Graphs, NISTIR 7788, September 2011. [NIST 

Computer Security Division]

Accepted 

1. G. S. Abo, Y. K. Hong, B. C. Choi, M. J. Donahue, et al., Micromagnetic Computer Simulated 

Scaling Effect of S-shaped Permalloy Nanoelement on Operating Fields for AND or OR Logic, IEEE Transactions on Magnetics. 

2. I. Beichl, E. Moseman, and F. Sullivan, Computing Network Reliability Coefficients, Congressus 

Numerantium. 

3. J. D. Benson, Stability Analysis of Several Nondilute Multiple Solute Transport Equations, Journal of Mathematical Chemistry.
Summary of Activities for Fiscal Year 2011 101 

4. J. D. Benson, C. C. Chicone, and J. K. Critser, A 

General Model for the Dynamics of Cell Volume, 

Global Stability, and Optimal Control, Journal of 

Mathematical Biology.

5. J. Benson, A. J. Kearsley, and A. Z. Higgins, 

Mathematical Optimization of Procedures for Cryoprotectant Equilibration Using a Toxicity Cost 

Function, Cryobiology. 

6. J. W. Bullard, C. F. Ferraris, E. J. Garboczi, N. S. 

Martys, P.E. Stutzman, and J.E. Terrill, Virtual 

Cement and Concrete, Innovations in Portland 

Cement Manufacturing, Portland Cement Association. 

7. H. S. Cohl, Table Errata to Formulas and Theorems for the Special Functions of Mathematical 

Physics, by Magnus, Oberhettinger & Soni (1966), 

Mathematics of Computation. 

8. B. Cloteaux and L. A. Valentin, Counting the 

Leaves of Trees, Congressus Numerantium. 

9. B. Cloteaux, Extracting Hierarchies with Overlapping Structure from Network Data, in Proceedings 

of the Winter Simulation Conference, Phoenix AZ, 

December 11-14, 2011. 

10. H. S. Cohl and E. G. Kalnins, Fourier and Gegenbauer Expansions for a Fundamental Solution of 

the Laplacian in the Hyperboloid Model of Hyperbolic Geometry, Journal of Physics A. 

11. G. Dogan and R. H. Nochetto, First Variation of 

the General Curvature-dependent Energy, ESAIM: 

Mathematical Modelling and Numerical Analysis. 

12. W. L. George, N. S. Martys, and J. E. Terrill, 

Computational Rheology for Cement and Concrete, Workshop on High-Performance Computing 

for Industry, Rensselaer Polytechnic Institute. 

13. C. Hagwood, J. Bernal, M. Halter, and J. Elliott, 

Evaluation of Segmentation Algorithms on Cell 

Populations Using CDF Curves, IEEE Transactions on Medical Imaging. 

14. P. D. Hale, J. Jargon, C. M. J. Wang, B. Grossman, M. Claudius, J. L. Torres, A. Dienstfrey, and 

D. Williams, A Statistical Study of De-Embedding 

Applied to Eye Diagram Analysis, IEEE Transactions on Instrumentation and Measurement. 

15. D. Harris, F. Sullivan, and I. Beichl, Linear Algebra and Sequential Importance Sampling for 

Network Reliability, in Proceedings of the Winter 

Simulation Conference, Phoenix AZ, December 

11-14, 2011. 

16. R. Kacker, R. Kessel, and K.-D. Sommer, Only 

Non-informative Bayesian Prior Distributions 

Agree with the GUM Type A Evaluations of Input 

Quantities, in Proceedings of the Conference on 

Advanced Mathematical and Computational Tools 

in Metrology and Testing (AMCTM 2011).

17. A. Kearsley, T. Gruendling, C. Barner-Kowollik, 

W. Wallace, and C. Guttman, Automated Data 

Processing of and Quantification in Polymer Mass 

Spectrometry, Mass Spectrometry in Polymer 

Chemistry. 

18. R. Kessel and R. Kacker, Monte Carlo Simulations 

Using Parallel Computing and a Client-server 

Model, in Proceedings of the Conference on Advanced Mathematical and Computational Tools in 

Metrology and Testing (AMCTM 2011). 

19. R. Kessel and R. Kacker, Improved Adaptive Procedure to Determine the Necessary Number of 

Monte Carlo Trials to Achieve the Required Numerical Tolerance, in Proceedings of the 

Conference on Advanced Mathematical and Computational Tools in Metrology and Testing 

(AMCTM 2011). 

20. Z. H. Levine, B. R. Galloway, A. P. Peskin, C. P. 

Heussel, and J. J. Chen, Theoretical Limits of RECIST in Medical CT as a Measure of Tumor 

Volume, Medical Physics. 

21. Y.-K. Liu, Universal low-rank matrix recovery 

from Pauli measurements, in Proceedings of Neural Information Processing Systems (NIPS). 

22. L. Ma, O. Slattery, and X. Tang, Single Photon 

Frequency Up-conversion and Its Applications in 

Quantum Information Systems, in Proceedings of 

the Single Photon Workshop 2011. 

23. V. Marbukh, Robust Cross-Layer Network Optimization for Diverse QoS Requirements: Work in 

Progress, World Congress on Engineering 2011. 

24. V. Marbukh, K. Sayrafian, H. Mahboubi, A. Momeni, Ahmadreza, A. Aghdam, An Efficient 

Target Monitoring Scheme with Controlled Node 

Mobility for Sensor Networks, IEEE Transactions 

on Control Systems Technology.

25. V. Marbukh, From TCP Effective Bandwidth to 

Internet Performance, IFIP Performance 2011. 

26. N. S. Martys, C. F. Ferraris, W. L. George, S. G. 

Satterfield, M. T. Olano, Computational Based 

Study of Suspension Flow in a Vane Rheometer, 

83rd Annual Meeting of the Society of Rheology. 

27. W. F. Mitchell and M. A. McClain, A Survey of 

hp-Adaptive Strategies for Elliptic Partial Differential Equations, Annals of the European Academy 

of Sciences. 

28. J. S. Sims, G. W. Bryant, W. L. George, T. G. 

Griffin, J. G. Hagedorn, J. T. Kelso, T. M. Olano, 
 102 NIST Applied and Computational Mathematics Division 

A. P. Peskin, S. G. Satterfield, and J. D. Terrill, 

Computation and Visualization of Nano-structures 

and Nano-optics, Computing and Visualization in 

Science. 

29. O. Slattery, L. Ma, and X. Tang, Towards Narrow 

Linewidth Non-degenerate Correlated Photon 

Pairs, in Proceedings of the Single Photon Workshop 2011. 

30. J. C. Wu, A. Martin, C. Greenberg, and R. Kacker, 

Measurement Uncertainties in Speaker Recognition Evaluation, SPIE Defense, Security, and 

Sensing Conference, Orlando, FL, April 25-29, 

2011. 

31. Y. Zhang, E. Knill, and S. Glancy, Asymptotically 

Optimal Confidences for Rejecting Local Realism, 

Physical Review A. 

In Review 

1. B. K. Alpert, W. B. Doriese, J. W. Fowler, and J. 

N. Ullom, Predicted Energy Resolution of a Running-Sum Algorithm for Microcalorimeters. 

2. J. D. Benson, C. C. Chicone, and J. K. Critser, 

Analytical Optimal Controls for the State Constrained Addition and Removal of Cryoprotective 

Agents.

3. J. D. Benson, C. T. Benson, and J. K. Critser, 

Mathematical Model Formulation and Validation 

of Water and Cryoprotective Agent Transport in 

Whole Hamster Pancreatic Islets.

4. G. W. Bryant, N. Malkova, J. Sims, M. Zielinski, 

W. Jaskolski, and J. Aizpurua, Controlling the Optics of Quantum Dots with Nanomechanical Strain. 

5. T. J. Burns, S. P. Mates, R. L. Rhorer, E. P. 

Whitenton, and D. Basak, On Modeling the Peak 

Temperature on the Tool-chip Interface During 

High-speed Machining of AISI 1045 Steel. 

6. B. Cloteaux, Graphical Approximations of Degree 

Sequences.

7. H. S. Cohl and E. G. Kalnins, Fundamental Solution of the Laplacian in the Hyperboloid Model of 

Hyperbolic Geometry. 

8. H. S. Cohl, On a Generalization of the Generating 

Function for Gegenbauer Polynomials. 

9. D. L. Cotrell, P. A. Lott, and G. B. McFadden, 

Boundary Slip Effects on the Stability of Spiral 

Poiseuille Flow. 

10. W. B. Doriese, B. K. Alpert, J. W. Fowler, G. C. 

Hilton, A. S. Hojem, K. D. Irwin, C. D. Reintsema, D. R. Schmidt, G. M. Stiehl, D. S. Swetz, J. N. 

Ullom, and L. R. Vale, Optimization of the Detector-bias Circuit for a TES X-ray Microcalorimeter 

in a Multiplexed Array. 

11. T. Gerrits, M. Stevens, B. Baek, B. Calkins, A. 

Lita, S. Glancy, E. Knill, S.W. Nam, R. Mirin, R. 

Hadfield, R. Bennink, W. Grice, S. Dorenbos, T. 

Zijlstra, T. Klapwijk, and V. Zwiller, Generation 

and Characterization of Degenerate, Factorizable, 

Pulsed Squeezed Light at Telecom Wavelengths 

from pp-KTP. 

12. X. Han, Y. Liu, J. D. Benson, and J. K. Critser, A 

Calorimetric Method to Measure Watercryoprotectant Mutual Diffusivity in Biological 

Tissues at Both Super- and Sub-zero Temperatures.

13. D. Harris, F. Sullivan, and I. Beichl, Fast Sequential Importance Sampling to Estimate the Graph 

Reliability Polynomial. 

14. R. D. Johnson, III, K. K. Irikura, R. Kacker, and R. 

Kessel, Response to Comments by Pernot and 

Cailliez. 

15. N. Martys, M. Khalil, W. George, D. Looten, and 

P. Hebraud, Stress Propagation in Colloidal Suspensions under Shear. 

16. M. Mullan and E. Knill, Improving Quantum 

Clocks via Semidefinite Programming. 

17. D. P. O’Leary and B. W. Rust, Variable Projection 

for Nonlinear Least Squares Problems. 

18. J. S. Pelc, L. Ma, C. R. Phillips, Q. Zhang, C. 

Langrock, O. Slattery, X. Tang, M. M. Fejer, 

Long-wavelength-pumped Upconversion Singlephoton Detector at 1550 nm: Performance and 

Noise Analysis. 

19. M. T. Rakher, L. Ma, M. Davanço, O. Slattery, X. 

Tang, and K. Srinivasan, Spectral and Temporal 

Manipulation of Single Photons from a Quantum 

Dot by Pulsed Frequency Upconversion. 

20. S. Ressler, Integrating jQuery with 3D Descriptive 

Markup of X3DOM. 

21. W. Wang, Y. Lei, S. Sampath, R. Kacker, R. 

Kuhn, and J. Lawrence, A Combinatorial Approach to Building Navigation Graphs for 

Dynamic Web Applications. 

22. D. F. Williams, M. T. Ghasr, B. Alpert, Z. Shen, 

A. Arsenovic, R. M. Weikle II, and R. Zoughi, 

Improved Calculation of the Reflection Coefficient 

of Radiating Rectangular-Waveguide Test Ports. 

23. J. C. Wu, A. F. Martin, and R. N. Kacker, Studies 

of Nonparametric Two-Sample Bootstrap in ROC 

Analysis on Large Datasets. 
Summary of Activities for Fiscal Year 2011 103 

Sponsored Research 

24. Milan Bradonjić and Iraj Saniee, Bootstrap Percolation on Random Geometric Graphs. [AlcatelLucent Bell Labs]

25. Iraj Saniee and Gabriel H. Tucci, Scaling of Congestion in Small World Networks. [Alcatel-Lucent 

Bell Labs]

26. Alonso Silva and Gabriel H. Tucci, On the Spectral Characteristics of Ad-hoc Networks and their 

Mobility Properties. [Alcatel-Lucent Bell Labs]

Presentations 

Invited Talks 

1. I. Beichl, Sequential Importance Sampling for 

Network Problems, Bell Laboratories, Murray 

Hill, NJ, April 26, 2011. 

2. J. D. Benson, Modeling and Optimization in Cryobiology, Northwestern University, Evanston, IL, 

Nov. 8, 2010. 

3. R. Bohn, NIST Cloud Computing Program, Texas 

Advanced Computing Center (TACC), Austin, 

TX, May 4, 2011. 

4. R. Bohn, Cloud Computing Standards, Business of 

Cloud Computing Forum, San Diego, CA, June 

15, 2011. 

5. R. Boisvert, Mathematics at NIST, Keene State 

College, Keene, NH, Apr. 15, 2011. 

6. J. W. Bullard, N. S. Martys, J.-L. Traore, W. L. 

George, and S. G. Satterfield, Computer Models as 

Guides through Material Design Space, International Congress on the Chemistry of Cement,

Madrid, Spain, July 3-8. 

7. T. Burns, On Modeling the Constitutive Response 

of Carbon Steel for High-speed Machining Simulations, Plasticity 2011, Vallarta, Mexico, January 

3-8, 2011. 

8. H. S. Cohl, The Fourier and Gegenbauer Analysis 

of Fundamental Solutions for the Polyharmonic 

Equation on Riemannian Spaces of Constant Curvature, Gdansk University of Technology, Gdansk, 

Poland, August 16, 2011. 

9. A. Dienstfrey, Dynamic Calibration for Dynamic 

Metrology, 6th Dynamic Metrology Workshop, 

Gothenburg, Sweden, June 20-22, 2011. 

10. J. Fong, A Risk-Informed Approach to Asset 

Management of Aging Engineered Systems, University of Wisconsin, Madison, WI, Oct. 13, 2010. 

11. J. Fong, A Risk-Informed Approach to Asset 

Management of Aging Engineered Systems, University of Houston, Houston, TX, Oct. 19, 2010. 

12. J. Fong, A Risk-Informed Approach to Asset 

Management of Aging Engineered Systems, Pacific Northwest National Laboratory, Richland, WA, 

Nov. 15, 2010. 

13. J. Fong, A New Approach to Verification and Validation (V&V) of Codes using a Statistical Plug-in 

for Uncertainty Estimation, U.S. Department of 

Energy Training Workshop on Waste Processing 

Models: Material Properties Standards and Software Verification and Validation, Germantown, 

MD, Nov. 30, 2010. 

14. J. Fong, Uncertainty Estimation and Engineering 

Reliability, Composites Workshop IV, Stanford 

University, Palo Alto, CA, Jan. 24, 2011 

15. J. Fong, Uncertainty Estimation and Failure Prediction of Full-Scale Structures using a MultiScale Approach and a Public-Domain Statistical 

Software Package named DATAPLOT, University 

of South Carolina, Columbia, SC, April 29, 2011. 

16. J. Fong, Uncertainty Estimation and Failure Prediction of Full-Scale Structures using a MultiScale Approach, University of California, Irvine, 

CA, May 20, 2011. 

17. J. Fong, Uncertainty Estimation and Failure Prediction of Full-Scale Structures using a MultiScale Approach, First Global Forum on Structural 

Longevity, Orlando, FL, July 26, 2011. 

18. J. Fong, Uncertainty Estimation and Engineering 

Reliability, Department of Aeronautics and Astronautics, Composites Workshop IV, Stanford 

University, Stanford, CA, July 29, 2011. 

19. J. Fong, Design of Experiments and Modern Statistics for Life Estimation and Extension of FullScale New and Aging Structures, Universidade Estadual de Campinas (State University of 

Campinas), Sao Paulo, Brazil, Sept. 22, 2011. 

20. J. Fong, Design of Experiments and Modern Statistics for Life Estimation and Extension of FullScale New and Aging Structures, Embraer, Sao 

Paulo, Brazil, Sept. 23, 2011. 

21. J. Fong, NIST Research on Materials Science and 

Verification and Validation, Department of Mechanical Engineering, Universidade Federal Do 

Rio Grande Do Norte (Federal University of Rio 

Grande do Norte), Natal, Brazil, Sept. 26, 2011. 

22. J. Fong, Design of Experiments and Modern Statistics for Life Estimation and Extension of FullScale New and Aging Structures, Universidade 
 104 NIST Applied and Computational Mathematics Division 

Federal Do Rio Grande Do Norte (Federal University of Rio Grande do Norte), Natal, Brazil, Sept. 

26, 2011. 

23. J. Fong, Uncertainty Estimation and Failure Prediction of Full-Scale Structures using a MultiScale Approach and a Public-Domain Statistical 

Software Package named DATAPLOT, Universidade Federal Do Rio Grande Do Norte (Federal 

University of Rio Grande do Norte), Natal, Brazil, 

Sept. 27, 2011. 

24. W. L. George, N. S. Martys, and J. E. Terrill, 

Computational Rheology for Cement and Concrete, Workshop on High-Performance Computing 

for Industry, Rensselaer Polytechnic Institute, 

Troy, NY, Oct. 26, 2011. 

25. W. L. George, N. S. Martys, S. G. Satterfield, M. 

Olano, and J. E. Terrill, Simulating the Flow of 

Dense Suspensions, Argonne National Laboratory 

exhibit, SC Conference, Seattle WA, Nov. 15, 

2011. 

26. S. Jordan, Quantum Algorithms for Quantum Field 

Theories, Laboratory for Physical Science, College 

Park, MD, May 5, 2011. 

27. S. Jordan, Quantum Algorithms for Quantum Field 

Theories, Institute for Quantum Computation Waterloo, Canada, August 2, 2011. 

28. S. Jordan, Quantum Algorithms for Quantum Field 

Theories, Schloss Dagstuhl Seminar on Quantum 

Cryptanalysis, Wadern, Germany, Sept. 23, 2011. 

29. R. Kacker, High Strength Combinatorial Testing 

for Software and other Applications, Infosys 

Technologies Ltd., Bangalore, India, December 

29, 2010. 

30. R. Kacker, Evolution of Modern Approaches to 

Express Uncertainty in Measurement, Indian Institute of Technology-Madras, Chennai, India, Jan. 7, 

2011. 

31. R. Kacker, High Strength Combinatorial Testing 

for Software and other Applications, Indian Institute of Technology-Madras, Chennai, India, Jan. 

10, 2011. 

32. R. Kacker, Advanced Combinatorial Testing for 

Software and Systems, Technical University of 

Berlin, Berlin, Germany, June 27, 2011. 

33. R. Kacker, Advanced Combinatorial Testing for 

Software and Systems, Fraunhofer Institute for 

Open Communication Systems, Berlin, Germany, 

June 28, 2011. 

34. R. Kuhn and R. Kacker, Combinatorial Testing for 

Software and Systems, Institute for Defense Analyses, Arlington VA, Feb. 25, 2011. 

35. R. Kuhn and R. Kacker, Advanced Combinatorial 

Testing for Software and Systems, Army Test and 

Evaluation Command, March 30, 2011. 

36. R. Kuhn and R. Kacker, Advanced Combinatorial 

Testing for Software and Systems, Institute for Defense Analyses, April 6, 2011. 

37. R. Kuhn and R. Kacker, Advanced Combinatorial 

Testing for Software and Systems, Johns Hopkins 

University Applied Physics Lab, April 27, 2011. 

38. L. Ma, O. Slattery, and X. Tang, Single Photon 

Frequency Up-conversion and Its Applications in 

Quantum Information Systems, Single Photon 

Workshop 2011, PTB Braunschweig, Germany, 

June 27- 30, 2011. 

39. L. Ma, O. Slattery, and X. Tang, Pulsed-pumped 

Up-conversion Single Photon Detectors and Their 

Applications, SPIE Optics and Photonics, San Diego, CA, Aug. 21-25, 2011. 

40. W. F. Mitchell, Comparison of hp-Adaptive Finite 

Element Strategies, University of Maryland, College Park, MD, Sept. 20, 2011. 

41. D. P. O’Leary, Mathematics and Computer Science in Words and Images, Women in Science 

Forum, Towson University, March 2011. 

42. D. P. O’Leary, Where am I? Position from Incomplete Distance Information, Purdue University, 

April 2011. 

43. D. P. O’Leary, Mathematics in Words and Images, 

Norbert Wiener Lecture, Tufts University, March 

30, 2011. 

44. D. P. O’Leary, Uncertainty Quantification for IllPosed Problems, Norbert Wiener Lecture, Tufts 

University, March 31, 2011. 

45. D. P. O’Leary, Where am I? Position from Incomplete Distance Information, Norbert Wiener 

Lecture, Tufts University, April 1, 2011. 

46. D. P. O’Leary, Where am I? Position from Incomplete Distance Information, Householder 

Symposium, Lake Tahoe, CA, June 2011. 

47. D. P. O’Leary, Confidence in Image Reconstruction, IMA Workshop on Large-scale Inverse 

Problems and Quantification of Uncertainty, Minneapolis, MN, June 2011. 

48. A. Reid, Object-Oriented Finite Element Materials 

Modeling at NIST, 3rd International Conference 

on Computational Methods in Engineering and 

Science (FEMTEC 2011), Stateline, NV, May 9, 

2011. 
Summary of Activities for Fiscal Year 2011 105 

49. S. Ressler, 3D Computer Graphics and the World 

Wide Web, Florida International University, Miami, FL, Feb. 4, 2011. 

50. B. Saunders, Numerical Grid Generation Applied 

to Interactive Complex Function Visualization in 

the NIST Digital Library of Mathematical Functions, George Mason University, March 25, 2011. 

51. O. Slattery, L. Ma, and X. Tang, Towards Narrow 

Linewidth Non-degenerate Correlated Photon 

Pairs, Single Photon Workshop 2011, PTB Braunschweig, Germany, June 27- 30, 2011. 

52. O. Slattery, L. Ma, and X. Tang, Toward a Narrow 

Linewidth Non-degenerate Source of Correlated 

Photon Pairs, SPIE Optics and Photonics, San Diego, CA, Aug. 21-25, 2011. 

53. X. Tang, L. Ma, and O. Slattery, Photon Frequency Conversion and Its Applications, 20th

International Laser Physics Workshop, Sarajevo, 

July 11-15, 2011. 

54. X. Tang, Single Photon Frequency Up-conversion 

and Its Applications in Quantum Information Research at NIST, University of Maryland Baltimore 

County, Sept. 21, 2011. 

Conference Presentations 

1. B. K. Alpert, Improved High Rate Pulse Processing Algorithms for Microcalorimeters, 14th 

International Workshop on Low Temperature Detectors, Heidelberg, Germany, Aug. 2, 2011. 

2. T. Burns, On Modeling the Peak Temperature on 

the Tool-chip Interface during High-speed Machining of AISI 1045 steel, Eighth International 

Conference on High-Speed Machining, Metz, 

France, Dec. 8-10, 2010. 

3. T. Burns, Effect on Flow Stress of a Rapid Phase 

Transition in AISI 1045 Steel, ASME 2011 International Manufacturing Science and Engineering 

Conference, Corvallis, OR, June 13-17, 2011. 

4. A. Carasso, Effective Non-Uniqueness in Linear 

and Nonlinear Backward Parabolic Equations, 7th

International Congress on Industrial and Applied 

Mathematics, Vancouver, Canada, July 20, 2011. 

5. J. Chalfoun, A. Dima, A. P. Peskin, J. Elliott, and 

J. J. Filliben, A Human Inspired Local RatioBased Algorithm for Edge Detection in Fluorescent Cell Images, 6th International Symposium on 

Visual Computing, Las Vegas, NV, Nov. 29 – Dec. 

1, 2010. 

6. B. Cloteaux, Modeling Affiliations in Networks, 

Winter Simulation Conference, Baltimore, MD, 

Dec. 8, 2010. 

7. B. Cloteaux, Counting the Leaves of Trees, 

SECGTC 2011, Boca Raton, FL, March 9, 2011. 

8. H. S. Cohl, Gegenbauer and Fourier Series for 

Fundamental Solutions of the Laplacian and Powers in Hyperspherical Coordinate Systems Which 

Parametrize Points in Euclidean and Hyperbolic 

Space, February Fourier Talks, University of 

Maryland, Feb. 17-18, 2011. 

9. H. S. Cohl and E.G. Kalnins, Radial Fundamental 

Solutions of Laplace’s Equation on Riemannian 

Spaces of Constant Curvature, Special Functions 

and Orthogonal Polynomials of Lie Groups and 

Their Applications, Decin, Czech Republic, Aug. 

14-20, 2011. 

10. H. S. Cohl, Logarithmic Fourier Series for a Fundamental Solution of the Polyharmonic Equation 

in Even-dimensional Euclidean Space, 11th International Symposium on Orthogonal Polynomials, 

Special Functions and Applications, Leganes, 

Spain, Aug. 29-Sept. 2, 2011. 

11. G. Dogan, Fast Optimization Method for the 

Chan-Vese Model in Image Segmentation, SIAM 

Conference on Computational Science and Engineering, Reno, NV, February 28 – March 4, 2011. 

12. G. Dogan, Simultaneous Segmentation and Reconstruction of Piecewise Constant Functions, 7th

International Congress on Industrial and Applied 

Mathematics, Vancouver, BC, Canada, July 19, 

2011. 

13. M. Donahue, Parallelizing a Micromagnetic Program for Multi-processor Non-uniform Memory 

Access Computers, Conference on Magnetism and 

Magnetic Materials, Atlanta, GA, Nov. 15, 2010. 

14. S. Glancy, E. Knill, M. Girard, F. Mallet, and T. 

Gerrits, Lessons and Innovations in Maximum 

Likelihood Quantum State Tomography, Southwest Quantum Information and Technology 

Workshop, Boulder, CO, Feb. 17, 2011. 

15. T. M. Hanna, E. Tiesinga, W. F. Mitchell and P. S. 

Julienne, Bound States of Interacting Polar Molecules in an Optical Lattice, 42nd Annual DAMOP 

Meeting, Atlanta, GA, June 14. 

16. F. Y. Hunt, A Mathematical Model of a Computer 

Protocol, Class of 1902 Lecture, Oxtoby Centennial Conference, Bryn Mawr College, Bryn Mawr 

PA., October 2, 2010. 

17. F. Y. Hunt, Spectral Based Methods That Streamline the Search for Failure Scenarios in Large-
 106 NIST Applied and Computational Mathematics Division 

Scale Distributed Systems, 19th IASTED International Conference on Applied Simulation and 

Modeling, Crete, Greece, June 22-24, 2011.

18. F. Y. Hunt, A Mathematical Model of Joint Congestion Control and Routing in Multisource 

Networks, IEEE International Conference on Control Applications, Denver, CO, Sept. 29, 2011. 

19. R. Kacker and J. Lawrence, Trapezoidal and Curvilinear Trapezoidal Distributions which arise in 

Metrology, International Conference on Mathematical Sciences, St. Thomas College, Pala, 

Kerala, India, January 3-5, 2011. 

20. R. Kacker, R. Kuhn, E. Miranda and J. Aldrich, 

Evolution of Advanced Combinatorial Testing for 

Software and Systems from Design of Experiments, Carnegie Mellon University Master of 

Software Engineering Professional Program, Pittsburgh, PA, June 7, 2011. 

21. A. Kearsley and J. Benson, Time-Optimal Boundary Control of a State Constrained Bio-mass 

Transport Systems, 7th International Congress on 

Industrial and Applied Mathematics, Vancouver, 

Canada, July 21, 2011. 

22. R. Kessel, R. Kacker, and K.D. Sommer, Uncertainty Budgeting for Range Calibration, 

Measurement Systems and Process Improvement, 

National Physical Laboratories, Teddington, UK, 

April 19-20, 2010. 

23. Y.-K. Liu, Quantum Property Testing for Bounded-Degree Graphs, Workshop on Approximation, 

Randomization, and Combinatorial Optimization 

(APPROX-RANDOM), Princeton, NJ, Aug. 17-19, 

2011. 

24. D. Lozier, The NIST Handbook of Mathematical 

Functions: What Do Statisticians Want?, International Conference on Mathematical Sciences, St. 

Thomas College, Pala, Kerala, India, Jan. 3-5, 

2011. 

25. V. Marbukh, Robust Cross-layer Network Optimization for Diverse QoS Requirements: Work in 

Progress, International Conference of Applied and 

Engineering Mathematics, London, UK, July 6-8, 

2011. 

26. V. Marbukh, Towards Modeling Effect of Multiscale Stochastic Dynamics on Flow-Level 

Queuing Performance in the Internet, 7th International Congress on Industrial and Applied 

Mathematics, Vancouver, Canada, July 18-22, 

2011. 

27. V. Marbukh, Cooperative Sensor Relocation in a 

Mobile Sensor Network by Distributed Subgradient Algorithm, Fifth International Conference on 

Sensor Technologies and Applications (SENSOCOMM 2011), Nice, France, Aug. 21-26, 2011. 

28. W. F. Mitchell and M. A. McClain, Performance 

of hp-Adaptive Finite Element Methods, SIAM 

Conference on Computational Science and Engineering, Reno, NV, Feb. 27 – Mar. 4, 2011. 

29. W. F. Mitchell and M. A. McClain, Comparison of 

hp-Adaptive Finite Element Strategies, Workshop 

on Multiresolution and Adaptivity in Numerical 

PDEs, Foundations of Computational Mathematics, Budapest, Hungary, July 13, 2011. 

30. W. F. Mitchell and M. A. McClain, Comparison of 

hp-Adaptive Finite Element Strategies, 24th 

Chemnitz FEM Symposium, Holzhau, Germany, 

Sept. 29, 2011. 

31. E. Moseman, Computing Network Reliability Coefficients, 42nd Southeastern International 

Conference on Combinatorics, Graph Theory, and 

Computing, Boca Raton, FL, March 7-11, 2011. 

32. M. Mullan, Improving Quantum Clocks via Semidefinite Programming, Southwest Quantum 

Information and Technology Workshop, Boulder, 

CO, Feb. 17-20, 2011. 

33. A. Peskin, A. Dima, J. Chalfoun, and J. Elliot, 

Predicting Segmentation Accuracy for Biological 

Cell Images, Bioimage Informatics 2010, Pittsburg, PA, Sept. 17-19, 2010. 

34. A. Peskin, A. Dima, Modeling Clinical Tumors to 

Create Reference Data for Tumor Volume Measurement, 6th International Symposium on Visual 

Computing, Las Vegas, NV, Nov. 29 – Dec. 1, 

2010. 

35. A. Peskin, A. Dima, J. Calfoun, J. Elliott, Predicting Segmentation Accuracy for Biological Cell 

Images, 6th International Symposium on Visual 

Computing, Las Vegas, NV, Nov. 29 – Dec. 1, 

2010. 

36. A. P. Peskin, D. J. Hoeppner, and C. H. Stuelten, 

Segmentation and Cell Tracking of Breast Cancer 

Cells, 7th International Symposium on Visual 

Computing, Las Vegas, NV, Sept. 26-28, 2011. 

37. B. Rust and D. P. O’Leary, The Variable Projection Method – Back to the Roots, 7th International 

Congress on Industrial and Applied Mathematics, 

Vancouver, Canada, July 19, 2011. 

38. B. Saunders, The NIST Digital Library of Mathematical Functions: A New Resource for 

Mathematical and Physical Scientists, Fall Meeting of the MD-DC-VA Section of the Mathematics 

Association of America, George Mason University, 

Fairfax, VA, Nov. 6, 2010. 
Summary of Activities for Fiscal Year 2011 107 

39. W.-B. Yang, K. Sayrafian-Pour, J. Hagedorn, J. 

Terrill, K. Y. Yazdandoost, A. Taparugssanagorn, 

M. Hamalainen, and J. Iinatti, Impact of an Aortic 

Valve Implant on Body Surface UWB Propagation: A Preliminary Study, Fifth International 

Symposium on Medical Information and Communication Technology (ISMICT), March 27-31, 

2011. 

40. Y. Zhang, E. Knill, and S. Glancy, Computable 

and Asymptotically Optimal Lower Bounds on 

Confidence for Rejecting Local Realism Given 

Experimental Data, Southwest Quantum Information and Technology Workshop, Boulder, CO, 

Feb. 17, 2011. 

Web Services 

1. Digital Library of Mathematical Functions18: a 

repository of information on the special functions 

of applied mathematics. 

2. Guide to Available Mathematical Functions19: a 

virtual repository of mathematical software components. 

3. Matrix Market20: a repository of matrices for testing of algorithms and software for numerical linear 

algebra. 

4. SciMark21: a benchmark for scientific computing 

in Java. 

Software Released22

1. NGraph++23: a small, C++ class library for the 

analysis of network graphs. Version 3.9. – R. Pozo

2. Equiv++24: a template C++ package for mathematical equivalence. New. – R. Pozo

3. LaTeXML25: a LaTeX to XML converter. Multiple 

releases. – B. Miller 

4. OOF226: Object Oriented Finite Elements, modeling of materials with complex microstructures. 

Version 2.1.5 – S. Langer

 

18 http://dlmf.nist.gov/ 19 http://gams.nist.gov/ 20 http://math.nist.gov/matrixmarket/ 21 http://math.nist.gov/scimark/ 22 In cases where multiple versions have been released during the 

year we only list the last. 

23 http://math.nist.gov/~RPozo/ngraph/index.html 24 http://math.nist.gov/~RPozo/ngraph/ngraph_toolkit_index.html 25 http://dlmf.nist.gov/LaTeXML 26 http://www.nist.gov/mml/ctcms/oof/

5. PHAML27: Parallel Hierarchical Adaptive MultiLevel, general purpose software for 2D elliptic 

partial differential equations. Version 1.9.1 – W. 

Mitchell

6. Tcl packages Itcl 3.4.1 and 4.0b7, and Thread 

2.6.7 – D. Porter

7. Tcl/Tk28: Tool Command Language and Toolkit. 

Version 8.5.10 and 8.6b2 – D. Porter

8. PCrawler29: suite of Python modules to build network graphs by crawling the World Wide Web. 

Version 3.0 – R. Pozo

9. Local Realism Analysis Engine:30 standardizes the 

quantification and comparison of experiments that 

demonstrate failure of local realism with quantum 

states and measurements – Y. Zhang, M. Knill, and 

S. Glancy 

Conferences, Minisymposia, 

Lecture Series, Shortcourses 

MCSD Seminar Series 

1. J. Benson (NIST), Modeling and Optimization in 

Cryobiology, Oct. 19, 2010. 

2. I. Saniee (Bell Laboratories), The Large Scale 

Curvature of Networks and its Implications for 

Network Management and Security, Nov. 9, 2010. 

3. M. Cromer, Jr. (University of Delaware), Modeling and Simulation of a Complex Fluid: Wormlike 

Micellar Solutions, Nov. 30, 2010. 

4. E. Fried (McGill University), Dynamical Equations for the Contact Line During the Evaporation 

or Condensation of a Sessile Drop, Jan. 21, 2011. 

5. T. Mohan (INFOSYS Technologies), Leveraging 

Cloud for Software Assurance, March 18, 2011. 

6. J. Rinzel (New York University), Dynamics of 

Perceptual Bistability, March 29, 2011. 

7. A. Sidi (Israel Institute of Technology), Extrapolation Methods for Vector Sequences with 

Applications to Large-Scale Problems, April 5, 

2011. 

8. A. Nurse (NIST and the University of Maryland), 

A Model of Force Generation in a Three Dimensional Toroidal Cluster of Cells, April 19, 2011. 

 

27 http://math.nist.gov/phaml/ 28 http://tcl.sourceforge.net/ 29 http://math.nist.gov/~RPozo/ngraph/webcrawler.html 30 http://arxiv.org/abs/1108.2468
 108 NIST Applied and Computational Mathematics Division 

9. A. Gray (Georgia Institute of Technology), Machine Learning on Massive Data Sets, April 26, 

2011. 

10. M. Mascagni, (Florida State University), The 

Scalable Parallel Random Number Generators 

(SPRNG) Library and Modern Computer Architectures, May 4, 2011. 

11. P. Johansson (National Cancer Institute, National 

Institutes of Health), A Genomic Portrait of Tumor 

Progression Using Second Generation Sequencing, 

May 24, 2011. 

12. A. Gueye (NIST and the University of Maryland), 

Game Theoretic Modeling, Analysis, and Mitigation of Security Risks, June 7, 2011. 

13. B. Amidan (Pacific Northwest National Laboratories), Typical Patterns, Atypical Events, and 

Uncertainty in Complex Systems, Sept. 15, 2011. 

Hosted Public Events 

1. R. Boisvert, Member, Organizing Committee, 

From Quantum Information and Complexity to 

Post Quantum Information Security, University of 

Maryland, October 27-29, 2010. 

2. R. Boisvert, Chair, Organizing Committee, IFIP 

Working Conference on Uncertainty Quantification in Scientific Computing, Boulder, CO, Aug. 

1-4, 2011. 

3. A. Dienstfrey, Chair, Program Committee, IFIP 

Working Conference on Uncertainty Quantification in Scientific Computing, Boulder, CO, Aug. 

1-4, 2011. 

4. D. Lozier, Chair, Organizing Committee, International Conference on Special Functions in the 21st

Century: Theory and Applications, Washington, 

DC, April 6-8, 2011. 

External Events Organization 

1. R. Boisvert and E. Knill, Members, Program 

Committee, Workshop: From Quantum Information and Complexity to Post Quantum 

Information Security, Joint Quantum Institute, 

College Park, MD, Oct. 27-29, 2010. 

2. B. Cloteaux, Session Organizer, Winter Simulation 

Conference, Dec. 11-14, 2011.

3. G. Dogan, Co-Organizer, Minisymposium on 

Scientific Computing in Image Processing, SIAM 

Conference on Computational Science and 

Engineering, Reno, NV, February 28 – March 4, 

2011. 

4. J. Fong, Symposium Organizer, PVP Conference, 

Baltimore, MD, July 17-22, 2011.

5. F. Hunt, Member, Organizing Committee, 5th Infinite Possibilities Conference, University of 

Maryland, Baltimore County, March 2012. 

6. A. Kearsley and J. Benson, Co-Organizers, Minisymposium on Mathematical Modeling and 

Optimization in Cryobiology, 7th International 

Congress on Industrial and Applied Mathematics, 

Vancouver, Canada, July 18-22, 2011. 

7. V. Marbukh, Co-Organizer, NIST-Bell Labs 

Workshop on Large-Scale Geometry of Networks, 

Bell Labs, Murray Hill, NJ, April 26, 2011. 

8. G. McFadden, Co-Organizer, Memorial Conference for Paul R. Garabedian, New York 

University, December, 2010. 

9. W. Mitchell, Member, Scientific Committee, International Conference of Numerical Analysis and 

Applied Mathematics (ICNAAM 2011), Halkidiki, 

Greece, Sept. 19-25, 2011. 

10. D. P. O’Leary, Member, Organizing Committee, 

SIAM Conference on Applied Linear Algebra 

(LA12), Valencia, Spain, June 18-22, 2012. 

11. Y. Parker and J. Terrill, Co-Organizers, NIST 

booth, SC10, the 2010 International Conference 

for High Performance Computing, Networking, 

Storage and Analysis, New Orleans, LA, Nov. 13-

19, 2010. 

12. Y. Parker and J. Terrill, Co-Organizers, NIST 

booth, SC11, the 2011 International Conference 

for High Performance Computing, Networking, 

Storage and Analysis, Seattle, WA, Nov. 13-19, 

2010. 

13. B. Rust and K. Mullen, Co-Organizers, 

Minisymposium on Recent Advances in Separable 

Nonlinear Least Squares, 7th International 

Congress on Industrial and Applied Mathematics, 

Vancouver, Canada, July 18-22, 2011. 
Summary of Activities for Fiscal Year 2011 109 

Other Professional Activities 

Internal 

1. I. Beichl, NIST Research Advisory Committee. 

2. R. Boisvert, NIST Scientific Computing Steering 

Group. 

3. R. Boisvert, ITL Diversity Committee. 

4. S. Glancy, NIST Boulder SURF Committee. 

5. W. Mitchell, ITL Awards Committee. 

6. A. O’Gallagher, ITL Diversity Committee. 

7. A. Peskin, Boulder Research Advisory Council. 

8. S. Ressler, NIST Lobby Display Advisory Council. 

External 

Editorial 

1. I. Beichl, Editor-in-Chief, Computing in Science & 

Engineering. 

2. J. Benson, Associate Editor, CryoLetters. 

3. R. Boisvert, Associate Editor, ACM Transactions 

on Mathematical Software. 

4. R. Boisvert, Editor, Numerical Analysis, Mathematical Software, and Computational Engineering, 

Finance, and Science areas, Computing Research 

Repository (CoRR) preprint service.31

5. A. Dienstfrey, Associate Editor, International 

Journal of Uncertainty Quantification. 

6. D. Lozier, Associate Editor, Journal of Numerical 

Analysis, Industrial and Applied Mathematics. 

7. G. McFadden, Associate Editor, Journal of Crystal 

Growth. 

8. G. McFadden, Associate Editor, Interfaces and 

Free Boundaries. 

9. W. Mitchell, Associate Editor, Journal of Numerical Analysis, Industrial and Applied Mathematics. 

10. D. P. O’Leary, Editor-in-Chief, SIAM Journal on 

Matrix Analysis and Applications. 

11. D. P. O’Leary, Member, Editorial Board, Education Section , SIAM Review. 

12. D. P. O’Leary, Member, Editorial Board, SIAM 

Books. 

 

31 http://www.arXiv.org/

13. D. P. O’Leary, Member, Editorial Board, Computing in Science & Engineering. 

14. D. P. O’Leary, Department Editor, Your Homework Assignment, Computing in Science & 

Engineering. 

15. R. Pozo, Associate Editor, ACM Transactions on 

Mathematical Software. 

Boards and Committees 

1. I. Beichl, Member, IEEE Electronic Products and 

Services Subcommittee. 

2. J. Benson, Member, Planning Committee, Society 

for Cryobiology. 

3. R. Bohn, Member, Cloud Computing Scoping 

Subcommittee, President’s National Security Telecommunications Advisory Committee (NSTAC). 

4. R. Bohn. Co-chair, Faster Administration of Science and Technology Education and Research 

(FASTER) Community of Practice, Networking 

and Information Technology R&D (NITRD) Program. 

5. R. Boisvert, Chair, International Federation for 

Information Processing’s (IFIP) Working Group 

2.5 (Numerical Software). 

6. R. Boisvert, Co-chair, Publication Board, Association for Computing Machinery (ACM). 

7. R. Boisvert, Member, Program Review Committee, Center for Computing Sciences, Institute for 

Defense Analysis. 

8. R. Boisvert, Member, External Review Committee, Computer Science Department, George 

Washington University. 

9. R. Boisvert, Member, Fast Track Action Committee on Modeling and Simulation, Office of Science 

and Technology Policy. 

10. E. Knill, Member, Technical Advisory Panel, 

Quantum Computer Science Program, IARPA. 

11. D. Lozier, Secretary, Activity Group on Orthogonal Polynomials and Special Functions, Society for 

Industrial and Applied Mathematics (SIAM). Term 

ended December 2010. 

12. D. Lozier, Member, Steering Committee, Painleve 

Project. 

13. D. P. O’Leary, Chair, Committee on Committees, 

Association for Women in Mathematics. 

14. D. P. O’Leary, Member, Oversight Committee, 

Gene Golub SIAM Summer Schools, 2010-2014. 
 110 NIST Applied and Computational Mathematics Division 

15. B. Miller, Member, Math Working Group, WWW 

Consortium. 

16. D. Porter, Member, Tcl Core Team. 

17. S. Ressler, Member, Declarative 3D for the Web 

Architecture Community Group32. 

18. B. Saunders, Member, MAA Committee on Business, Industry, and Government Mathematics. 

19. J. Terrill, Member, Federal High End Computing 

Implementation Task Force. 

20. J. Terrill, Member, High End Computing Research 

and Development, and Infrastructure Interagency 

Working Groups, Networking and Information 

Technology R&D (NITRD) Program. 

Reviewing 

Division staff members referee manuscripts for a wide 

variety of journals including ACM Transactions on 

Mathematical Software, Acta Materialia, The Annals of 

Applied Statistics, BIT, Computational Statistics and 

Data Analysis, Inverse Problems, Computer Physics 

Communications, European Physical Journal D: Atomic, Molecular, Optical and Plasma Physics, IEEE 

Transactions on Information Theory, IEEE Transactions on Instrumentation & Measurement, IEEE 

Transactions on Magnetics, International Journal of 

Uncertainty, Journal of Applied Physics, Journal of 

Computational and Applied Mathematics, Journal of 

Computational Physics, Journal of Fluid Mechanics, 

Journal of Mathematical Analysis and Applications, 

Mathematical Reviews, Mathematics of Computation, 

Nature, New Journal of Physics, Numerical Mathematics, Numerical Methods for Partial Differential 

Equations, Optical Engineering, Optics Communications, Physical Review, Physical Review A, Physical 

Review B, Physical Review Letters, Quantum Information and Computation, SIAM Journal on Matrix 

Analysis and Applications, SIAM Journal of Scientific 

Computing. 

In addition, Division staff members served as reviewers for a variety of conferences, including 2011 

Winter Simulation Conference, QIP (Quantum Information Processing) 2011, 22nd Annual IEEE 

International Symposium on Personal, Indoor and Mobile Radio Communications 2011 (PIMRC’11), 

Symposium on the Foundations of Computer Science 

(FOCS).

ACMD staff also reviewed proposals for the following agencies/competitions during FY 2011: DOE, 

Netherlands Organization for Scientific Research, NSF. 

 

32 http://www.w3.org/community/declarative3d/

External Contacts 

ACMD staff members make contact with a wide variety of organizations in the course of their work. 

Examples of these follow. 

Industrial Labs 

21st Century Medicine 

Agilent 

Alcatel-Lucent Bell Laboratories 

Balance R&D (Australia) 

CD-adapco 

CLO Virtual Fashion, Inc. 

Enig Associates 

ExactData, LLC 

Google Summer of Code 

Gradient Effects 

IBM Entity Analytics 

Intel 

The Jackson Laboratory 

Northrop Grumman 

Orbital Sciences Corporation 

Palantir Technologies 

Plastic Technologies Inc. 

Synarch 

Tech-X Corporation 

Volume Graphics GmbH 

Government/Non-profit Organizations 

Aberdeen Proving Grounds 

Army Research Lab 

Association for Computing Machinery 

Association for Women in Mathematics 

Cambridge Healthtech Institute 

CNRS/ESPCI, France 

DARPA 

Department of Energy 

Ecole Nationale Superieure de Chimie de Rennes 

(France) 

Environmental Protection Agency 

IARPA 

IDA Center for Computing Sciences 

IEEE Computer Society 

Institute for Mathematics and Its Applications 

Lawrence Livermore National Laboratory 

Leibniz Inst. for Solid State and Matls. Res. (Germany) 

Library of Congress 

Maui High Performance Computing Center 

NASA Goddard Space Flight Center 

NASA Langley Research Center 

National Institutes of Health 

National Physical Laboratory (UK) 

Nuclear Decommissioning Authority (UK) 

Nuclear Regulatory Commission 

National Security Agency 
Summary of Activities for Fiscal Year 2011 111 

Oak Ridge National Laboratory 

Office of Science and Technology Policy 

Pacific Northwest National Laboratory 

Royal Melbourne Institute of Technology 

Sandia National Laboratories 

Santa Fe Institute 

Society for Industrial and Applied Mathematics 

Swedish Metrology Institute 

Theiss Research 

World Wide Web Consortium 

Universities 

Boston University 

California Institute of Technology 

Cambridge University 

College of William and Mary 

Concordia University (Canada) 

Cornell University 

Delft University of Technology (The Netherlands) 

Durham University (UK) 

Frederick University (Cyprus) 

George Mason University 

George Washington University 

Georgia Institute of Technology 

Heriot-Watt University (UK) 

Indiana University 

Jacobs University, Bremen (Germany) 

Johns Hopkins University 

King Abdullah Univ. of Sci. and Tech. (Saudi Arabia) 

Linkoping University (Sweden) 

Murdoch University (Australia) 

New York University 

Oregon State University 

Polish Academy of Science 

Renssalear Polytechnic University 

State University of New York at Binghamton 

University of Antwerp (Belgium) 

University of Birmingham (UK) 

University of California, Davis 

University of Colorado 

University of Connecticut 

University of Delaware 

University of Luxembourg 

University of Maryland 

University of Maryland Baltimore County 

University of Minnesota 

University of Nebraska -- Lincoln 

University of Nevada, Reno 

University of New Mexico 

University of Oulu (Finland) 

University of Pittsburgh 

University of Sheffield (UK) 

University of South Africa 

University of Texas at Arlington 

University of Technology (The Netherlands) 

University of Utah 

University of Virginia 

University of Wisconsin 

Virginia Tech
 112 NIST Applied and Computational Mathematics Division 
Summary of Activities for Fiscal Year 2011 113 

Part V: Appendix 

 Part V 

 Appendix 
 114 NIST Applied and Computational Mathematics Division 
Summary of Activities for Fiscal Year 2011 115 

Staff 

ACMD consists of full time permanent staff located at NIST laboratories in Gaithersburg, MD and Boulder, CO. This is supplemented with a variety of special appointments. The following list reflects all 

appointments held during any portion of the reporting period. (*) Denotes staff at NIST Boulder. 

Division Staff 

Ronald Boisvert, Chief, Ph.D. (Computer Science), Purdue University, 1979 

Robin Bickel, Secretary 

Robert Bohn, Ph.D. (Physical Chemistry), University of Virginia, 1991 

Alfred Carasso, Ph.D. (Mathematics), University of Wisconsin, 1968 

Roldan Pozo, Ph.D. (Computer Science), University of Colorado at Boulder, 1991 

Christopher Schanzle, B.S. (Computer Science), University of Maryland Baltimore County, 1989 

Mathematical Analysis and Modeling Group 

Timothy Burns, Leader, Ph.D. (Mathematics), University of New Mexico, 1977 

*Bradley Alpert, Ph.D. (Computer Science), Yale University, 1990 

*Andrew Dienstfrey, Ph.D. (Mathematics), New York University, 1998 

Jeffrey Fong, Ph. D. (Applied Mechanics and Mathematics), Stanford University, 1966 

David Gilsinn, Ph.D. (Mathematics), Georgetown University, 1969 

Fern Hunt, Ph.D. (Mathematics), New York University, 1978 

Raghu Kacker, Ph.D. (Statistics), Iowa State University, 1979 

Anthony Kearsley, Ph.D. (Computational and Applied Mathematics), Rice University, 1996 

Peter Ketcham. M.S. (Mathematics), University of Minnesota, 1997 

Geoffrey McFadden, NIST Fellow, Ph.D. (Mathematics), New York University, 1979 

*Agnes O’Gallagher, M.S. (Applied Mathematics), University of Colorado at Boulder, 1991 

Bert Rust, Ph.D. (Astronomy), University of Illinois at Urbana-Champaign, 1974 

 NRC Postdoctoral Associates 

James Benson, Ph.D. (Mathematics), University of Missouri – Columbia, 2009 

NIST-ARRA Postdoctoral Fellows 

Asha Nurse, Ph.D. (Mechanical Engineering), Brown University, 2011 

Ismet Sahin, Ph.D. (Electrical and Computer Engineering), University of Pittsburgh, 2006 

 Faculty Appointee (Name, Degree / Home Institution)

Daniel Anderson, Ph.D. / George Mason University 

Saul Gass, Ph.D. / University of Maryland College Park 

Dianne O’Leary, Ph.D. / University of Maryland College Park 

Florian Potra, Ph.D. / University of Maryland Baltimore County 

Guest Researchers (Name, Degree / Home Institution)

Mirit Aladjem, Ph.D. / National Institutes of Health 

Richard Braun, Ph.D. / University of Delaware 

Guillaume Bousquet / ISIMA, Campus de Clermont-Ferrand, France 

David Cotrell, Ph.D. / Lawrence Livermore National Laboratory 

*John Gary, Ph.D. / NIST (retired) 

Katharine Gurski, Ph.D. / George Washington University 

Rüdiger Kessel, Ph.D. / Metrodata GmbH, Germany 

Sohyoung Kim, Ph.D. / National Institutes of Health 

Yu (Jeff) Lei, Ph.D. / University of Texas at Arlington 
 116 NIST Applied and Computational Mathematics Division 

P. Aaron Lott, Ph.D. / Lawrence Livermore National Laboratory 

Bruce Murray, Ph.D. / SUNY Binghamton 

Asha Nurse, Ph.D. / University of Maryland (ARRA Postdoctoral Fellow) 

Sita Ramamurti, Ph.D. / Trinity Washington University 

Ismet Sahin, Ph.D. / University of Maryland (ARRA Senior Fellow) 

Christoph Witzgall, Ph.D., NIST Scientist Emeritus

Mathematical Software Group 

Daniel Lozier, Leader, Ph.D. (Applied Mathematics), University of Maryland, 1979 

Javier Bernal, Ph.D. (Mathematics), Catholic University, 1980 

Valerie Coffman, Ph.D. (Physics), Cornell University, 2006 

Michael Donahue, Ph.D. (Mathematics), Ohio State University, 1991 

Stephen Langer, Ph.D. (Physics), Cornell University, 1989 

Marjorie McClain, M.S. (Mathematics), University of Maryland College Park, 1984 

Bruce Miller, Ph.D. (Physics), University of Texas at Austin, 1983 

William Mitchell, Ph.D. (Computer Science), University of Illinois at Urbana-Champaign, 1988 

Donald Porter, Ph.D. (Electrical Engineering), Washington University, 1996 

Bonita Saunders, Ph.D. (Mathematics), Old Dominion University, 1985 

NRC Postdoctoral Associates 

Howard Cohl, Ph.D. (Mathematics), University of Auckland, 2010 

Faculty Appointees (Name, Degree / Home Institution)

Frank Olver, D.Sc. / University of Maryland College Park 

G.W. Stewart, Ph.D. / University of Maryland College Park 

Abdou Youssef, Ph.D. / George Washington University 

Guest Researchers (Name, Degree / Home Institution)

Gunay Dogan, Ph.D. / Theiss Research 

Leonard Maximon, Ph.D. / George Washington University 

Qiming Wang / NIST (retired) 

Computing and Communications Theory Group 

Ronald Boisvert, Acting Leader 

 Isabel Beichl, Ph.D. (Mathematics), Cornell University, 1981 

Brian Cloteaux, Ph.D. (Computer Science), New Mexico State University, 2007 

*Scott Glancy, Ph.D. (Physics), University of Notre Dame, 2003 

Barry Hershman, A.A. (Electronics Engineering), Capitol College, 1979 

Stephen Jordan, Ph.D. (Physics), Massachussetts Institute of Technology, 2008 

 *Emanuel Knill, NIST Fellow, Ph.D. (Math), University of Colorado at Boulder, 1991 

 Yi-Kai Liu, Ph.D. (Computer Science), University of California, San Diego, 2007 

 Vladimir Marbukh, Ph.D. (Mathematics) Leningrad Polytechnic University, 1986 

Alan Mink, Ph.D. (Electrical Engineering), University of Maryland, 1980 

Oliver Slattery, M.S. (Electrical Engineering), Johns Hopkins University, 2008 

Xiao Tang, Ph.D (Physics), Chinese Academy of Sciences, 1985 

NRC Postdoctoral Associates 

Elizabeth Moseman, Ph.D. (Mathematics), Dartmouth College, 2007 

James Shook, Ph.D. (Mathematics), University of Mississippi, 2010 

NIST-ARRA Postdoctoral Fellows 

Assane Gueye, Ph.D. (Computer Science), University of California, Berkeley, 2011 
Summary of Activities for Fiscal Year 2011 117 

Contractors 

 Lijun Ma, Ph.D. (Optical Engineering), Tsinghua University, 2001 

Faculty Appointees (Name, Degree / Home Institution)

James Lawrence, Ph.D. / George Mason University 

Guest Researchers (Name, Degree / Home Institution)

Stephen Bullock, Ph.D. / IDA Center for Computing Sciences 

Robert Carpenter / NIST (retired) 

*Bryan Eastin, PhD. / Northrup Grumman 

Paulina Kuo, Ph.D. / Joint Quantum Institute, University of Maryland 

Francis Sullivan, Ph.D. / IDA Center for Computing Sciences 

Students (Name, Degree / Home Institution)

Amada Crawford / University of Colorado 

Mark Girard / Trinity University 

*Michael Mullan / University of Colorado at Boulder 

*Adam Meier / University of Colorado at Boulder 

*Yanbao Zhang / University of Colorado at Boulder 

High Performance Computing and Visualization Group 

Judith Terrill, Leader, Ph.D. (Information Technology), George Mason University, 1998 

Yolanda Parker, Office Manager 

William George, Ph.D. (Computer/Computational Science), Clemson University, 1995 

Terence Griffin, B.S. (Mathematics), St. Mary’s College of Maryland, 1987 

John Hagedorn, M.S. (Mathematics), Rutgers University, 1980 

John Kelso, M.S. (Computer Science), George Washington University, 1984 

*Adele Peskin, Ph.D. (Chemical Engineering), University of Colorado at Boulder, 1985 

Sandy Ressler, M.F.A. (Visual Arts), Rutgers University, 1980 

Steven Satterfield, M.S. (Computer Science), North Carolina State University, 1975 

James Sims, Ph.D. (Chemical Physics), Indiana University, 1969 

Faculty Appointees 

Marc Olano / University of Maryland Baltimore County 

Guest Researchers (Name, Degree / Home Institution)

Dennis Backhaus / Fachhochschule Wiesbaden (Germany) 

Styvens Belloge / ISIMA, Campus de Clermont-Ferrand, France 

Pradeep Gaddam / Core Projects and Technologies PVT LTD, India 

Stanley Hagstrom, Ph.D. / Indiana University 

Marlene Hildebrand / Polytech Nice-Sophia, France 

Clement Rey / ISIMA, Campus de Clermont-Ferrand, France 

Jean-Loup Traore / Université Blaise Pascal Clermont Ferrand II, France 

Students (Name / Home Institution)

Luis Catacora / Montgomery Blair High School 

Matthew Du / Thomas Wootton High School 

William Hess / Purdue University 

Kevin Rawlings / Carnegie Mellon University 

Anshu Rustagi / University of Illinois 

Poorva Singal / Franklin W. Olin College of Engineering 

Becky Song / Richard Montgomery High School 
 118 NIST Applied and Computational Mathematics Division 

Glossary of Acronyms 

A&S Abramowitz & Stegun (NBS Handbook of Mathematical Functions, 1964) 

ACM Association for Computing Machinery 

ACMD NIST/ITL Applied and Computational Mathematics Division 

ACTS Advanced Combinatorial Test Suites (software) 

AI artificial intelligence 

AISI American Iron and Steele Institute 

AMS American Mathematical Society 

ANSI American National Standards Institute 

ANTD ITL Advanced Networking Technology Division 

APD avalanche photo diode (photon detector) 

APS American Physical Society 

ARRA American Recovery and Reinvestment Act 

arXiv preprint archive housed at Cornell University (http://arxiv.org/) 

ASME American Society of Mechanical Engineers 

BAN body area network 

BLAS Basic Linear Algebra Subprograms 

CAIDA Cooperative Association for Internet Data Analysis 

Caltech Californial Institute of Technology 

CGM conjugate gradient method 

CI configuration interaction 

CMOS complementary metal-oxide semiconductor 

CNRS Centre National de la Recherche Scientifique 

CNST NIST Center for Nanoscale Science and Technology 

CODATA Committee on Data for Science and Technology 

CPA cryoprotective agent 

CPU central processing unit 

CPUT combinatorial-based prioritization for user-session-based testing 

CT combinatorial testing 

CT computed tomography 

CVSS Common Vulnerability Scoring System 

CY calendar year 

DARPA DOD Defense Advanced Research Projects Agency 

DIVERSE Device Independent Virtual Environments ― Reconfigurable, Scalable, Extensible (software) 

DLMF Digital Library of Mathematical Functions 

DNA deoxyribonucleic acid 

DOC Department of Commerce 

DOD U.S. Department of Defense 

DOE U.S. Department of Energy 

DPD dissipative particle dynamics 

DSPA distributed subgradient projection algorithm 

EL NIST Engineering Laboratory 

EPG error probability per gate 

ESPCI École Supérieure de Physique et Chimie Industrielles de la Ville de Paris 

FASTER Faster Administration of Science and Technology Education and Research 

FDA Food and Drug Administration 

FDS Fire Dynamics Simulator 

FEM finite element method 

FFT fast Fourier transform 

FY fiscal year 

F90gl Fortran 90 interface to OpenGL graphics standard 

GAMS Guide to Available Mathematical Software 

GCN Government Computer News 

GPS generalized processor sharing 

GUI graphical user interface 
Summary of Activities for Fiscal Year 2011 119 

HEC high-end computing 

HIM helium ion microscope 

HTML hypertext markup language 

Hy-CI Hylleraas-Configuration Interaction technique 

IAS information assurance and security 

IDA Institute for Defense Analysis 

IEEE Institute of Electronics and Electrical Engineers 

IFIP International Federation for Information Processing 

IMS Innovations in Measurement Science 

INCITE Innovative and Novel Computational Impact on Theory and Experiment (DOE Program) 

ISIMA Institut Supérieur d'Informatique, de Modélisation et de leurs Applications (France) 

IT information technology 

ITL NIST Information Technology Laboratory 

JILA joint NIST-University of Colorado physics research institute 

JAMA Java Matrix package (software) 

LaTeX a math-oriented text processing system 

LaTeXML LaTeX to MathML translator 

MAA Mathematical Association of America 

MALDI/TOF matrix assisted laser desorption/ionization time-of-flight (mass spectrometer) 

MathML Mathematical Modeling Language (W3C standard) 

MGI Materials Genome Initiative 

MIT Massachusetts Institute of Technology 

MKM mathematical knowledge management 

MLE maximum likelihood estimation 

MML NIST Material Measurement Laboratory 

MPI Message Passing Interface 

MRAM magneto-resistive random access memory 

MRI magnetic resonance imaging 

MSN mobile sensor network 

muMAG Micromagnetic Activity Group 

NASA National Aeronautics and Space Administration 

NBS National Bureau of Standards 

Ngraph Network Graph (software) 

NIH National Institutes of Health 

NIR near infrared 

NIST National Institute of Standards and Technology 

NISTIR NIST Internal Report 

NITRD Networking and Information Technology Research and Development 

NL The Netherlands 

NRC National Research Council 

NSF National Science Foundation 

NUM network utility maximization 

NUMA non-uniform memory access 

NVD National Vulnerability Database 

NYU New York University 

OOF Object-Oriented Finite Elements (software) 

OOMMF Object-Oriented Micromagnetic Modeling Framework (software) 

OSPF open shortest path first 

PDE partial differential equation 

PHAML Parallel Hierarchical Adaptive Multi Level (software) 

PML NIST Physical Measurement Laboratory 

PPLN periodically poled lithium niobate 

PREP Professional Research Experience Program 

PTB Physikalisch-Technische Bundesanstalt 

QD quantum dot 

QDPD quarternion-based dissipative particle dynamics 

QIS quantum information science 
 120 NIST Applied and Computational Mathematics Division 

QKD quantum key distribution 

QoS quality of service 

R&D research and development 

REGEN software for modeling of cryocoolers 

RIP restricted isometry property 

RF radio frequency 

SBIR Small Business Innovative Research 

SEM scanning electron microscope 

SHIP NIST Summer High School Internship Program 

SIAM Society for Industrial and Applied Mathematics 

SIGGRAPH ACM Special Interest Group on Graphics 

SIS sequential importance sampling 

SparseLib++ software for spare linear algebra in C++ 

Spblas sparse basic linear algebra subprograms 

SPIE International Society for Optical Engineering 

SRM standard reference material 

STEP NIST Student Temporary Employment Program 

SUNY State University of New York 

SURF Student Undergraduate Research Fellowship 

SVT singular value thresholding 

TES transition-edge sensor 

TNT Template Numerical Toolkit (software) 

TPM transition probability matrix 

TSA Transportation Security Administration 

TV total variation 

UCSD University of California at San Diego 

UK United Kingdom 

UMBC University of Maryland Baltimore County 

URL universal resource locator 

UTA University of Texas at Arlington 

UWB ultra-wide band 

VRML virtual reality modeling language 

W3C World Wide Web Consortium 

WebGL Web-based Graphics Library 

X3D Extensible 3D 

X3DOM an open-source frameword for integrating X3D and HTML5 

XML Extensible Markup Language